When a man is called to the Torah, he is called as his father’s son (eg, Yitzhak ben Avraham). When a person is sick and a misheberach is made, he is blessed as his mother’s child (eg, Yitzhak ben Sarah) So, if both parents’ names are used in the course of a person’s life -- albeit in different circumstances -- it would seem logical that at a bris or when a baby girl is named, the kriyat hashem would include both parents: (eg, Viyikarei sh’mo biyisrael Yitzhak ben Avraham viSarah). Historically, though, this has not been done. Why not? Is there a clear halachic reason that babies have traditionally been given just their fathers’ names at birth, or is it, rather, a matter of custom? Thank you very much.
To my understanding - reference to the person in a Klal aspect - in public form or matters is done with the father's name, whereas reference in the personal context is done with the mother's name. Rabbi Ro'i Margalit