The term talmid chacham is used commonly in our tradition to describe a Jew with a certain high level of knowledge, understanding, closeness to Gd, etc. Can the halachic label "talmid chacham" be used appropriately in our times?
The halachic term is indeed applied even today (although the qualification is debatable). Rema (YD 243:2) rules that all laws relating to a TC apply even today save for the penalty for embarrassing a TC (see PT Bava Kama 8:6). Others disagree and maintain that even today this penalty applies (Shach, CM, 1:19).
Koheles Rabbah 7:14 (Warsaw) applies the label to anyone who abandons his dealings to learn, or, alternatively, to one who can answer a halachic query regarding something he has previously learned.
איזהו תלמיד חכם רבי אבהו בשם רבי יוחנן כל שהוא מבטל עסקיו מפני משנתו תני כל ששואלן אותו הלכה ממשנתו ומשיב עליה
Who is a Talmid Chacham? R’ Avahu said in the name of R’ Yochanan: Anyone who abandons his dealings because of his learning. It was taught in a Braisa: anyone that we can ask him a Halacha from his learning and he can respond regarding it.
Eitz Yosef there explicitly writes that this has several halachic applications; for instance, a Talmid Chacham is presumed not to claim something as his unless he is 100% positive it is, and so he doesn’t need to provide simanim on a lost object (BM 23b-24a).
I can think of dozens of people who fit either or both of these definitions.
One who learns wisdom is considered a Talmud Chacham (a student of wisdom) The Sages were considered Talmidei Chachamim in their own day because they considered 1) scripture, 2) the science of their day and 3) the mentality of the generation at hand when concluding halacha. The Gemara displays page after page of examples of how these scholars derived to their conclusions.
Today we mainly have students that just learn of the halachic conclusions from the past but ignore the sciences, characteristics, and makeup of our own generation.
אמר ר' חייא בר אבא אמר ר' יוחנן אין צדיק נפטר מן העולם עד שנברא צדיק כמותו שנאמר (קהלת א, ה) וזרח השמש ובא השמש עד שלא כבתה שמשו של עלי זרחה שמשו של שמואל הרמתי (אמר) ר' חייא בר אבא א"ר יוחנן ראה הקדוש ברוך הוא שצדיקים מועטין עמד ושתלן בכל דור ודור שנא' (שמואל א ב, ח) כי לה' מצוקי ארץ וישת עליהם תבל
Apropos the righteous, Rabbi Ḥiyya bar Abba said that Rabbi Yoḥanan said: No righteous person departs from this world until another comparable righteous person is created, as it is stated: “And the sun rises and the sun sets” (Ecclesiastes 1:5); before the sun sets the new sun has already risen. Before the sun of Eli was extinguished, the sun of Samuel of Ramah had already shone (see I Samuel, chapter 3), and so on throughout the generations. And Rabbi Ḥiyya bar Abba said that Rabbi Yoḥanan said: The Holy One, Blessed be He, saw that righteous people were few, so He arose and planted some of them in each and every generation to ensure the presence of at least one righteous person in each generation. As it is stated: “For the pillars of the earth are the Lord’s, and He has set the world upon them” (I Samuel 2:8). Since the world rests upon the righteous, each generation requires the presence of a righteous person to provide that support.