The Jewish Messiah has many Names and titles. One of His many Names is Immanuel (Emmanuel when Romanized). But This Person of Whom we speak went by the quite ordinary name Yeshua (Jesus, in the Greek).
Thus, one might say that Miriam/Mary is the mother of “Yeshua” or “Jesus”.
Hope this helps.
As I read the Hebrew, I notice the gender of the verb translated by KJV "and shall call" is feminine as in "and she will call his name" which is identical to the verb in Genesis where it is prophesied by the angel to Hagar that she will bear a son and call his name Ishmael. The point is that Isaiah makes it clear the virgin will call bear a son and call him "God with us." She is the mother of the name(s) she names him.