No one says that his "earlier" names were erased from the Torah. In fact Moshe's Birth Certificate points out a medrash that Moshe had 10 different names. However, calling him Moshe was a reward for the daughter of Par'o who saved him and raised him with the midos to become Moshe Rabbeinu. There is also a medrash that he was called Tov or Tuviah from the pasuk speaking of his birth (Shmos 2:2).
וַתַּהַר הָאִשָּׁה וַתֵּלֶד בֵּן וַתֵּרֶא אֹתוֹ כִּי טוֹב הוּא
וַתִּצְפְּנֵהוּ שְׁלשָׁה יְרָחִים
2 The woman conceived and bore a son, and [when] she saw him that he
was good, she hid him for three months.
Moshe's Birth Certificate
The Midrash relates that Moshe had 10 names. His father called him
Chever, his mother called him Yekutiel, his sister Miriam called him
Yet the name given by Pharaoh's daughter was the one chosen by G-d.
The Chumash never refers to him by any name other than Moshe. Why?
Pharaoh's daughter saved Moshe's life and adopted him and cared for
him as her very own son. Therefore, she merited that her name
prevailed. Moshe himself may have used this name out of gratitude to
Another reason the Torah calls him Moshe is the significance of the
name itself. The name "Moshe" means that just as he was rescued and
drawn from the water, so too he will he rescue others from hardship,
and that is what he did.
Shemot Rabbah 1:26
Vayikrah Rabbah 1:3