There are certainly many names and titles by which the Messiah is called. As well as "Emmanuel", Isaiah has in 9:6 (ESV):
For to us a child is born,
to us a son is given;
and the government shall be upon his shoulder,
and his name shall be called
Wonderful Counselor, Mighty God,
Everlasting Father, Prince of Peace.
Aquinas says (Summa Theologica 3.37.2 ad 1):
All these names in some way mean the same as Jesus, which means "salvation." For the name Emmanuel, which being interpreted is "God with us," designates the cause of salvation, which is the union of the Divine and human natures in the Person of the Son of God, the result of which union was that "God is with us." 1
He therefore sees no real contradiction, since both names/titles are apt ways to speak about the same person. (He does not distinguish here between a name and a title, though he of course acknowledges that "Jesus" is the proper name of Jesus.)
John Calvin (Commentariorium in Isaiam prophetam) investigates the meaning of "and (she) shall call" (וְקָרָ֥את) in the Hebrew text of Isaiah. He asserts that the giving of a name, in Hebrew custom, was reserved to the father, and so since it is the mother who is doing the calling here, she must be doing something other than giving the child its regular everyday name. Calvin says she is announcing it like a herald (in hoc nomine promulgando, virginem fore instar praeconis), and it is a designation which is far more splendid than any mere man could have. This all points to it being something other than an ordinary personal name. He further notices (Commentarius in harmoniam evangelicam) that in Matthew, the verb is "they shall call", indicating the shared faith of all believers in the fact and purpose of the Incarnation. If we are all doing the calling together, then it sounds a lot less like the bestowing of a personal name, and a lot more like the recognition of the nature of Jesus, in the form of calling him by a particular special title.
1. in omnibus illis nominibus quodammodo significatur hoc nomen Iesus, quod est significativum salutis. Nam in hoc quod dicitur Emmanuel, quod interpretatur, nobiscum Deus, designatur causa salutis, quae est unio divinae et humanae naturae in persona filii Dei, per quam factum est ut Deus esset nobiscum.