Although it sounds exactly like the Russian diminutive form of Mary, the Jewish name Masha is actually of Biblical extraction. Tradition has it that the first Masha was named after a departed male named Moshe (Moses).1

One upshot is that originally "Masha" was spelled in Hebrew as מַשה. Had it had non-Hebrew roots, it would have been spelled משא, following the rules for transliterating non-Hebrew names into Hebrew.2

Yours truly,

Rabbi Menachem Posner