The first thing to keep in mind when considering the identities of Gog and Magog is to remember that their explicit mention is found primarily in the Prophets (Yechezkel chapter 38 and 39 and Zechariah chapter 14). Their genealogical root is also listed in Bereshit 10:2 as being descendants of Yaphet ben Noach.
The importance of this idea is that the books of the Prophets were chosen by the men of the Great Assembly from among many other prophetical books because those prophecies were relevant to and applicable to each and every generation. Like with the book of Bereshit, they are paradigms and not simply historical records.
So in that context, the identities of Gog and Magog can be different throughout history.
This answer will be limited to the perspective of where we stand today, in terms of current events and the scope of history as explained in the Torah.
Torah tradition lays out a framework for history that follows the general paradigm from the six days of Creation mentioned in Bereshit chapters 1 through 3. Like is explained in Tehillim, chapter 90 following the teaching of Moshe Rabbeinu, that framework establishes 1,000 years for each of the 6 days of Creation. That means that our current time cycle, the focus of our current state of being, is anticipated to cover 6,000 years.
We currently stand in the year 5,784, which corresponds to Friday afternoon of the 6th day of Creation, erev Shabbat. Like is taught in Bereshit, the 24 hour cycle of a single day begins from the 12 hour cycle of night and the second half of each day, meaning from sunrise, is 12 hours of daylight. So the first 500 years of each millennium is associated with night and the second 500 years with daylight. Each hour is equated with approximately 41.66 years.
The complete and final redemption is equated with the onset of that first Shabbat and the coming of Moshiach corresponds with the 6th hour of daylight of the sixth day and the blowing of the soul into the nostrils of the already formed body of Adam HaRishon (Meaning our species of human, there were other species prior to our own.) which had been formed in the preceding hours of the sixth day. That hour corresponds to the year 5,750.
Moshiach is destined to correct or beautify what transpired with Adam, his wife and the Nachash (a prior species of humanoid) in regard to the fruit from the Tree of Knowledge of Good and its opposite; to bring in Shabbat correctly and to celebrate it in accordance with G-d's will and commandments. In this context, it should be noted that according to the text of the written Torah (Bereshit 2:9, 2:16-17, 3:1-6) the specific species of the Tree of Knowledge is unknown. It is simply referred to as a tree.
One of the best sources for a compendium and concise discussion of this process and the details of Moshiach's coming, the events and conflicts of Gog and Magog and also Armilus HaRasha, the Prosecutor השטן הזה, who is called by the non-Jewish people the Anti-Christ, is Sefer Avkat Rochel by the Rishon, Rabbeinu Makir ben Abba Mori of Lunel, Provence in southern France. This is actually a three volume book, but the first volume can also be found in almost complete form in Midrash Talpiot.
Avkat Rochel lays out 10 signs or events that Torah tradition teaches on this subject that cover the first appearance of Moshiach until the complete and final redemption.
The first of those signs is called the period of the birth pangs of Moshiach חבלי משיח, because it is compared to the pain and suffering associated with childbirth.
In context, these birth pains are the tikkun made by Moshiach and his generation and are the consequence from the transgressions from Adam's wife, Chava enumerated in Bereshit 3:16. This period is also the beginning of the Wars of Gog and Magog.
That the War of Gog and Magog is divided into 3 stages or time periods. In the context of the allegory of the labor pains, this corresponds to the 3 general stages of labor in the delivery of a human child. This is like is found in Midrash Shocher Tov and elsewhere to Tehillim chapter 118:10-12 which mentions all the nations surrounding me to make war with me and afflict me, three times. This idea of being surrounded by those that want to afflict me also corresponds to the physical manifestation of the contractions experienced during labor and delivery, which often originate from behind and encircle the abdomen of the mother.
That first stage (What is called the Stage of Early and Active Labor.) is described in the first 3 signs of Avkat Rochel. It describes the rise of the 3 leaders of the Axis Powers in World War II, Hitler, Mussolini and Hirohito, the condition of the Jewish people at that time and their increasing level of suffering and anxiety, and the events of the Holocaust itself in detail.
The second and third signs describes in graphic detail the detonation of the nuclear bombs over Hiroshima and Nagasaki to conclude the war in the Pacific and the resulting black rain and severe radiation sickness that kills hundreds of thousands when they drink that rainwater to quench their parched throats from the effects of the blast. The 3rd sign explicitly connects this event to Yoel the Prophet 3:3 which says:
וְנָֽתַתִּי֙ מֽוֹפְתִ֔ים בַּשָּׁמַ֖יִם וּבָאָ֑רֶץ דָּ֣ם וָאֵ֔שׁ וְתִֽימְר֖וֹת עָשָֽׁן׃
That the Pillars of Smoke are pillars in the shape of Date Palm trees דקל תמרים, which can also be described as the form as a mushroom cloud.
These pillars of smoke in the shape of Date Palm trees, signaling the beginning of the Wars of Gog and Magog, harken back to the unnamed Tree(s) of Knowledge of Good and its opposite. That in keeping with the teachings of Rabbi Moshe Cordovero in Pardes Rimonim, Sha'ar 25, Chapter 6 quoting Rabbi Shimon Bar Yochai in Tikkunei Zohar, Tikkun 51, the expression the Tree of Knowledge of Good and its opposite is actually referring to two distinct trees, one pertains to Good (and its supervising Angel) and the second pertaining to the opposite of Good (and its supervising Angel). Therefore, there are two bombs detonated, one at each of two locations and two separate clouds.
This is also discussed in detail by Rabbi Moshe Chaim Luzzato in his Tikkunim Chadashim (תיקונים חדשים לרמח״ל, תיקונא שיתין, ד״ה בשעתא דייתי גוג כו׳) which says that the light and fire of the sun (a literal description of a nuclear explosion) will be seen between the heavens and the earth. According to Ramchal, both Moshiach (ben Yosef) and Gog are present in the world at that time.
Those bombs were detonated on August 6 and August 9, 1945. So in that historical context, you can now look for actual historical figures.
As a reference point for later discussion, George H. W. Bush, the future 41st President of the United States was serving as a Naval Aviator from June 1942 through September 1945 and in the Pacific theater, where those bombs were detonated, starting in May 1945.
He was released from active duty in September 1945 and enrolled at Yale University completing his Bachelors Degree in 2 and 1/2 years in 1948. It was during that time that he was initiated into the Skull and Bones secret society at Yale and assigned the secret name, Magog, which is given to the initiate considered to have the most extensive sexual experience within the society as reported in an article from Atlantic Monthly and also mentioned at Wikipedia. It is in this sense that the Prophet adds the description of Presiding Head of Meshech and Tuval. (Yechezkel 38:1-2) נשיא ראש משך ותבל
That Meshech and Tuval have a connotation of both great wealth and sexual defilement and perversion like VaYikra 20:13.
His first born son, George W. Bush, who was destined to be the 43rd President of the United States, was born July 6, 1946 which means that he was conceived in October 1945, the same year that the atomic bombs were detonated over Hiroshima and Nagasaki.
It is at this point that it is relevant to point out that linguistically in Hebrew, the letter Gimmel ג is included in the grouping known as the seven Doubling Letters. They are comprised of: בגדכפר״ת.
This means they can either have a dagesh (a point) applied or not. When the letter has a dagesh, it has a hard plosive or doubled sound and when the dagesh is absent, the letter has a soft fricative sound. The Jews of Teiman still have the tradition for pronunciation of a soft fricative Gimmel. It is pronounced like the "G" in the name George or like the letter "J" in modern English. In that context, it should be noted that Gog and Magog גוג מגוג are all written with the soft Gimmel in the books of the Prophets.
Returning to Avkat Rochel, the 6th sign discusses the rise and fall of Josef Stalin and his treatment of the Jewish people. With the fall of Stalin comes the revelation of Moshiach ben Yosef to the whole world.
Following the analogy of the Stages of Labor, the transition from the first stage, active labor, to the second stage, the delivery of the baby, is characterized in the Torah to the special sign given to Shifra and Puah, the Hebrew Midwives, for an indication of the imminent birth of a child. That the thighs of the pregnant Mother in labor would cool, indicating danger to her physical life and her drawing close to death.
The 7th sign discusses the rise of the political leader of the Jews in Israel called Armilus HaRasha. It also details the second stage of the War of Gog and Magog which describes Operations Desert Shield and Desert Storm during 1991 which concluded on Purim.
The President of the United States at that time was George H. W. Bush. It was during this time that the Lubavitcher Rebbe publicized the now famous Yalkut Shimoni on Isaiah recounting how the entire world would be drawn into a war between the King of Persia (at that time, Saddam Hussein, the leader of Iraq who was rebuilding the ancient city of Babylon), the King of Arabia (the leader of Kuwait) and Aram, which the Rebbe said indicated the Super Power (רוממות) of that day (the United States) and which would be directed toward the Jews in Israel and that Moshiach would announce from the roof of the Beit HaMikdash, the message from G-d to the Jewish people to not be afraid because the time of the redemption had come!
It also states that an agent from Armilus tries to murder Moshiach ben Yosef and in fact, Moshiach ben Yosef dies during this period.
This attempt to murder Moshiach ben Yosef is related to the murder of the Lubavitcher Yeshiva Bachur, Ari Halberstam, HY"D by the Palestinian terrorist Rashid Baz on the Prospect Park Bridge in Brooklyn following the Purim massacre in Hebron by Baruch Goldstein. The passing of Moshiach be Yosef is associated with the passing of the Lubavitcher Rebbe on 3 Tammuz, 5754 (1994).
In relation to the stages of labor, this is the second stage which is the period when the actual delivery of the baby occurs. The head crowns and the baby takes its first breath of life. The Torah says it is at this moment that the soul dresses within the physical body paralleling the description of the creation of Adam HaRishon in Bereshit. From this point forward chronologically, is considered the Days of Moshiach according to the Torah.
This moment, when the soul (of Moshiach), which is described in kabbalistic sources, like Sefer Ohr HaChama by Rabbi Avaraham Azulai (Volume 2 on the Zohar, parshat Shemot 7b, beginning with the words, Rabbi Shimon stood, etc. ר״ש זקף וגו׳) as the fifth level of soul, Yechidah or the Neshamah of the Neshamah, dresses in the body of Moshiach ben Yosef (who is also called Ephraim, like Ephraim ben Yosef), he becomes aware of who he is. This episode which describes what would be called today experiencing a stroke, is actually detailed in Pesikta Rabbati, chapter 36, which says:
התחיל הקב"ה מתנה עמו ואומר הללו שגנוזים הם אצלך עונותיהם עתידים להכניסך בעול ברזל ועושים אותך (כעול) [כעגל] הזה שכהו עיניו ומשנקים את רוחך בעול ובעונותיהם של אילו עתיד לשונך לידבק בחיכך רצונך בכך אמר משיח לפני הקדוש ברוך הוא שמא אותו צער שנים רבות הם אמר לו הקדוש ברוך הוא חייך וחיי ראשי שבוע (את) [אחת] שגזרתי עליך אם נפשך עציבה אני טורדן מעכשיו אמר לפניו רבון העולמים בגילת נפשי ובשמחת לבי אני מקבל עלי על מנת שלא יאבד אחד מישראל ולא חיים בלבד (יושיע) [יושעו] בימי [אלא אף אותם שגנוזים בעפר ולא מתים בלבד יושעו בימי אלא אף אותם מתים שמתו מימות אדם הראשון עד עכשיו] ולא אילו בלבד אלא אף נפלים [יושעו בימי] ולא אילו בלבד יושעו בימי אלא (למי) [כל מי] שעלתה על דעתך להבראות ולא נבראו (בהם) בכך אני רוצה בכך אני מקבל עלי
The 8th and 9th signs deals with the transition from the second stage to the third and final stage of the Wars of Gog and Magog. This transition from the 7th to the 8th sign would begin from the day of the passing of the Lubavitcher Rebbe and spans the 7 year cycle (the Shemittah cycle) which is the subject of Sanhedrin 97a.
In the analogy to the process of labor, this is the delivery of the placenta, the afterbirth, following the actual delivery of the child. There are still mild contractions which push the placenta out of the birth canal. This process helps to eliminate risk of infection to the Mother. In Sefer Avkat Rochel it says this is the blowing of the Great Shofar mentioned in Isaiah 27:13.
It is completion of this transition that we experienced September 11, 2,001 and the bombing of the World Trade Centers in New York City and the Pentagon in Washington DC, which corresponds with the Hebrew year 5,761 exactly 7 years following the passing of the Lubavitcher Rebbe. This began under the Presidency of George W. Bush, the 43rd President of the United States. These events are recounted in the Zohar, parshat Balak 212b and the commentary Ohr Yakar of Rabbi Moshe Cordevero. As a consequence of this bombing, the wars in Afghanistan and Iraq began on Hoshanna Rabbah. This event, the beginning of these wars is mentioned explicitly in the Tur Shulchan Aruch. For related information, see here: https://judaism.stackexchange.com/a/64279/7303
This is also discussed explicitly in Sefer Chesed l'Avraham (by Rabbeinu Avraham Azulai), section Sod HaMikvah (Ma'ayan 2: Nahar 59) which states that this occurs in the year following 5,760, once the Mikvah is full and fit to eliminate the condition of Tumah (similar to the effects from the delivery of the placenta in the the third stage of labor). Rabbi Avraham says this time point is what is referred to in the Prophets as the time when Tumah will pass from the land (Zechariah 13:2).
וְהָיָה֩ בַיּ֨וֹם הַה֜וּא נְאֻ֣ם ׀ יְהֹוָ֣ה צְבָא֗וֹת אַכְרִ֞ית אֶת־שְׁמ֤וֹת הָֽעֲצַבִּים֙ מִן־הָאָ֔רֶץ וְלֹ֥א יִזָּכְר֖וּ ע֑וֹד וְגַ֧ם אֶת־הַנְּבִיאִ֛ים וְאֶת־ר֥וּחַ הַטֻּמְאָ֖ה אַעֲבִ֥יר מִן־הָאָֽרֶץ׃
Like his father, George W. Bush continued many of the policies of his father including efforts to pressure the government of Israel to relinquish territory to the Palestinians in order to establish the two-state solution, even dividing the Capitol city, Jerusalem.
It should be noted the Heavenly response to this that occurred in 2003 with the explosion of the Space Shuttle Columbia, one of the symbols of United States wealth, power and global leadership, as its trajectory passed over Palestine, Texas near the Texas home of then President Bush.
Avkat Rochel alludes to, among other things the expulsion of Gush Katif in 2005 (which also harkens back to Pillars of Smoke and the Tree of Knowledge of Good and its opposite through the settlements of Neve Dekalim נוה דקלים, Tel Katifa תל קטיפא and Katif קטיף) and the consequences afterward, which is what we are experiencing now. Armilus also dies during this time period and once again the entire world surrounds Israel to try to divide Israel and Jerusalem.
It is in this final context that George W. Bush, the son of George H.W. Bush came to Jerusalem in 2008 trying to coerce then Prime Minister Ehud Olmert into agreeing to a two-state solution with the Palestinian Authority and dividing Jerusalem between Israel and the Palestinians. It was during this trip that the now famous Megillat Bush was written and signed by the Nasi of the Nascent Sanhedrin, Rabbi Adin Even-Yisroel Steinsaltz, Rabbi Chaim Richman and others and presented to President Bush. It is in this scroll that President George W. Bush was specifically identified with Gog from Yechezkel the Prophet 38:1. For details of this content of this scroll, watch the following video from Rabbi Richman.
In the context of this scroll which was presented to President George W.Bush as the embodiment of Gog and Magog when he came with intent to divide the Land of Israel and its Capitol, Jerusalem, he was given a choice to be like Cyrus, King of Persia to unite the people Israel, its land and its Capitol or the opposite. He chose the opposite path and continued to pursue dividing Israel with the establishment of the Two-State Solution for the Palestinians. The consequence of that choice, as specified in the scroll, would determine both his fate and the fate of those with him, meaning his nation.
The close of his Presidency in 2008 witnessed the economy of the United States plunged into one of the deepest economic collapses since the Great Depression of the 1930s. Politically speaking, the country was overturned with the election the next year of Barack Obama (who, together with his Vice-President, Joseph Biden, extended a public and open invitation to the leadership of Iran in the way of his address celebrating Nowruz and its principal character, Haaji Firuz, a perversion of the story in Megillat Esther and another enemy of the people Israel, Haman, the Agagite. The evil one, who while leading Mordechai through Shushan, had the chamberpot filled with his wife's excrement dumped on him from the rooftop above, mistakenly, by his wife, Zeresh.) who was directly responsible for the strengthening of Iran and its nuclear ambitions together with the weakening of the United States leadership globally and domestically.
Only with the election of President Donald Trump and his efforts to unify the entire land of Israel and its Capitol (even moving the United States Embassy in Israel from Tel Aviv to Jerusalem), did the economy and global influence of the United States improve. It is no accident that the government of Israel minted commemorative coins honoring President Trump for his help to Israel and comparing him to Cyrus, King of Persia exactly as outlined in Megillat Bush for a possible positive destiny for Gog, Presiding Head of Meshech and Tuval. In that context, it should be noted that Gog is ultimately to be given a fitting burial place in the land of Israel like it states in Yechezkel 39:11.
For those who are more interested in listening to a discussion of this subject from a contemporary and prominent Rabbi who possesses great depth in Torah, this is a link to Rabbi Isser Zalman Weisberg discussing specifically the subject of the identity of Gog and Magog today.