John 17:5 ...
Jesus recognizes that the Word became Jesus (John 1:14).
Jesus recognizes that He really is the Word ...
who was in heaven at the very beginning.
It's all quite confusing, isn't it.
What makes things even worse is when John says:
"Jesus Christ has come in the flesh" (1 John 4:2).
The truth is ... the Word has come in the flesh (as Jesus Christ).
Evidently, he means ...
Jesus Christ was a man (flesh) and was in the world.
Maybe the answer to the confusion is that it is impossible to draw such a distinct line as you are drawing. And I'm not opposed to your premise, that the name of Jesus is intended to refer to the person who is both God and man. I just don't see where it is necessary. If Jesus is the name applied to the Word once He was incarnate, fine, but His existence is from eternity, not from conception. He was in the beginning with the Father.
I'd even go so far as to suggest that He was not the begotten Son until He was conceived in Mary (i.e., until He was actually begotten). But what point does that require? What difference does it make for you?