Moshe is a Hebrew name. As the Torah specifically writes. (he had an Egyptian name, mentioned in sources) So is Avraham – Av hamon goyim. And Sara too. While not written in the Torah, Chazal say its source, of course in Hebrew.
Regarding my name, however, you’re right. It’s comes from the Yiddish, froggeh, question. “Little”, I think, is a pure English word.