I am looking for an answer for the following question: Where do we find the source in the Tora that Eretz Hakodesh is another name for Eretz Yisroel? if you know the source I will greatly appreciate an answer.
The term "Eretz Hakodesh" doesn't appear in Tanach (and the term "Eretz Yisrael" in Tanach refers only to the territory of the Kingdom of Israel, i.e., the Ten Tribes, e.g., Chronicles 2:30:25)). A partial parallel may be found in the phrase "admat kodesh" in Zechariah 2:16. The same term appears in Shemot 3:5 but that doesn't refer to Eretz Yisrael (unless you hold the opinion that Mt. Sinai was in Eretz Yisrael).
However, it's very likely an ancient term, because the Greek version of the term appears in a few Hellenistic Jewish texts. For example, it appears once in 2nd Maccabees 1:7:
"In the year 169, the time of the reign of King Demetrius, we wrote to you concerning all the hardship that came upon us, with the betrayal of Jason and his cohorts in the the holy land, they sinned in the kingdom of Judah."
and Philo also used the Greek term in his writings. For example:
"Therefore Helicon, this scorpion-like slave, discharged all his Egyptian venom against the Jews; and Apelles his Ascalonite poison, for he was a native of Ascalon; and between the people of Ascalon and the inhabitants of the holy land, the Jews, there is an irreconcileable and neverending hostility although they are bordering nations."
for he and his people had incurred no slight danger, but they had reason to apprehend expulsion from their country, and slavery, and utter destruction, as impending not only over those who were dwelling in the holy land, but over all the Jews in every part of the world."
The Aramaic version of the phrase appears many times in the Zohar. For example:
"אָמַר רִבִּי יְהוּדָה זַכָּאָה חוּלָקֵיהּ מַאן דְּזָכֵי בְּחַיּיוֹי לְמִשְׁרֵי מָדוֹרָא בְּאַרְעָא קַדִּישָׁא. דְּכָל מַאן דְּזָכֵי לָהּ, זָכֵי לְאַנְגְּדָא מִטַּלָּא דִּשְׁמַיָּא דִּלְעֵילָּא, דְּנָחִית עַל אַרְעָא. וְכָל מַאן דְּזָכֵי לְאִתְקַשְּׁרָא בְּחַיּיוֹי בְּהַאי אַרְעָא קַדִּישָׁא, זָכֵי לְאִתְקַשְּׁרָא לְבָתַר בְּאַרְעָא קַדִּישָׁא עִלָּאָה."
Rabbi Yehuda said: Fortunate is the portion of he who deserves during his lifetime to make his dwelling in the Holy Land. All who merit it will cause the dew of the heaven above to continue to descend upon the earth, so all who deserve the Holy Land in this lifetime will later deserve the higher Holy Land.
See a list here.
According to Ohr Yitzchak Margalit in his essay in Hebrew "Commandments of the Land as an Expression of its Sanctity", p. 281. n. 49, while references to the holiness of the land are made in various Talmudic sources, the phrase does not appear there. It seems to have arisen during the Middle Ages and began to gain popularity particularly during the Crusades. It received another boost in popularity with the rise of the modern Zionist movement.
Margalit does not mention the appearances of the phrase in the Zohar, but the rise in popularity of the term may be related to the appearance of the Zohar in those days.1
The Hebrew version of the phrase (both in full spelling ארץ הקודש and in short spelling ארץ הקדש) appears only a few times in Genizah sources. One is undated and some are from the 16th century and onwards.
It should be noted that Rabbi Shaul Yisraeli was in agreement with what is now written in the Hebrew Wikipedia concerning the origins of the phrase, that it's not an originally Jewish term but a Latin Christian one, "Terra Sancta".
1 This is not a comment on the dating or authorship of the Zohar.