After anylyzing the term "Eretz Yisroel" I could only find it in 3 instances in Nach. Does the term "ארץ ישראל" ever appear in Tanach?
Why does the term Eretz Yisroel never appear in the Torah?
I would like to suggest that as we all know the Jews did not go into Eretz Yisroel until the times of Yehoshua. Prior to that it was known as Eretz Canaan. It first got the name Eretz Yisroel when the Jews settled it in the times of Yehoshua.
כד הוו זכאין ישראל אקרי ארעא על שמא דא ארץ ישראל כד לא זכו אקרי ארעא על שמא אחרא ארץ כנען
"When Israel was worthy, the land was called by their name, 'Eretz Yisrael." When they were not, it was called by a different name, 'Eretz Canaan.'"
Given that most of Tanach was written in response to the failings of the Jewish People (see Nedarim 22a: "had the Jewish People not sinned, they would have been given only the Five Chumashim and the Book of Yehoshua"), then that might explain why indeed "Eretz Canaan" is the prevalent term.
וכן היתה ארץ כנען בטרם בא ישראל אליה כי היתה ארץ שוקטת ולא היתה עובדת לשום מלך אחר... אבל אחר שבאו ישראל לארץ כנען היתה נותנת מס ועובדת מלכים אחרים בסורם מאחרי השם
"The Land of Canaan, too, before the Jews came to it, was a peaceful country, not subject to any other king... But after the Jews came to the land of Canaan, it had to pay tribute and be subservient to other kings, when they stopped following Hashem."
Other than that, though, there are also some positive reasons given for this designation:
The Canaanites deserved to have the land named for them, because (some of them) left voluntarily rather than oppose the Jews' entry. (Bamidbar Rabbah 17:3)
Our physical world is called "Eretz Canaan" (Ohr Hachaim to Gen. 23:2, citing Zohar Bereishis 80a - although I haven't found it there, but in Midrash Hane'elam 122b). He doesn't elaborate, but I think I recall seeing an idea (probably somewhere in Chassidus) that the Torah calls the Land by this name because it is a prototype of what we are to accomplish: to take the "land of Canaan," in both the specific and the general meanings of this term, and turn it into a holy land.