Oh, do not be so silly. "Annunciation Day" is the day on which the Angel Gabriel announced to the Blessed Virgin Mary that she was to be the Mother of God. This happened on some day, why complain about what we call it?
I cannot find the term "Mother of God" in the Bible.
Does God have a mother?
Jesus is God. Mary is the mother of Jesus. Therefore Mary is the Mother of God. This does not mean that Mary is the mother of Jesus' divinity but only that she is the mother of the one person Jesus who is both God and man. "Does God have mother?" Jesus is God and he has a mother, Mary, so the answer is yes.
So then (according to you) God has a mother.
Does God also have a father?
Does God have sisters and brothers?
Ultimately we are headed toward “the mystery” aspects of God in any such discussion. You have no place else to go.
That is not what the Bible is about when I read it.
The Bible is about revelation.
You are logically compelled to deny that when we get down.