The Bible is silent about the name of Sarah's mother. So are the Talmud and other ancient rabbinical texts as far as I can tell. However, a rabbinical authority in the current era, Rabbi Chaim Kanievski gives her name as Yiska Bas Tissa - Yiksa the daughter of Tissa. If this is right it gives us both the name of Sarah's grandmother as well has her mother. Yiksa is usually translated as Jennifer and is related to foresight. Tissa is related to receiving, taking, etc. However it could aslo be Tessa, which is related to "beholding" in Hebrew and "harvest" in Greek.
Rabbi Kanievski was characterized by the New York Times as "one of the greatest Talmudic interpreters of his generation and one of the most revered figures among the world’s ultra-Orthodox Jews." I can give no details as to his basis for saying this. It is discussed with few details here.