An angel appeared to Moses; not God the Father nor the Son.
If we try to understand this from a Western mind set, from our cultural perspective, it is difficult to understand. Not so from Middle Eastern thought. This is what is known as the "law of agency". "The main point of the Jewish law of agency is expressed in the dictum "A person's agent is regarded as the person himself" (Ned.72b; Kidd.41b)." The Encyclopedia of the Jewish Religion, Adama Books, New York, NY, 1986, pg.15. The angel that spoke from the bush was Yahweh's agent or representative. As such, he had full authority to not only speak in His name, but to appropriate His name as in Exodus 3:14-15;
And God said unto Moses, I AM THAT I AM: and he said, Thus shalt thou say unto the children of Israel, I AM hath sent me unto you.
Exo 3:15 And God said moreover unto Moses, Thus shalt thou say unto the children of Israel, YHWH God of your fathers, the God of Abraham, the God of Isaac, and the God of Jacob, hath sent me unto you: this is my name for ever, and this is my memorial unto all generations.
He was speaking exactly what Yahweh wanted him to say.
Yes, God wanted Moses to see His Son and know He is God, I AM.
That's why Jesus said -
Jesus said to them, “Most assuredly, I say to you, before Abraham was, I AM.” John 8:58
The same way He said these words -
Then God said, “Let there be light”; and there was light. Genesis 1:3
JLB