Did Jesus call himself by God's own name?

JOHN 8:58. Jesus said that before Abraham was born that he is and saw Abraham. He called himself, “I AM”, which is the name of God in Exodus 3:14. Therefore Jesus was God.
 
Jesus only said I AM before Abraham was. He didn’t say my name is I AM.

Jesus said, “I AM”, but he did not say, “I AM in the sense God meant it in Exodus.”
 
Jesus was telling us that he is in eternity and can see what happens in time and that was how he was able to see Abraham who had been dead for a long long time. (It could be that the Book of Revelation says that Jesus was the lamb that was killed since the foundation of the world in 13:8 meaning from the perspective of eternity). We have no right to assume that he meant the latter. He did not even call himself, “I AM,” like God did. It was God’s name revealed to Moses but Jesus does not use it as a name but as a way of saying he is a timeless being. He was just saying that he exists in eternity where there is no past or future. Christians argue that when the Jews heard these words they took them to mean that he believed himself to be God for it is recorded that they immediately picked up stones to fire at him. Death by stoning was the price for blasphemously claiming to be God under the Law. The validity of their argument rests on whether or not they are right to suppose that the Jews were going to kill Jesus by stoning over what he had said. Maybe they had no intention of stoning him to death. If they had, then note that the text does not say that they gathered the rocks with the assent of their conscience though it did tell them to liquidise any would-be gods. Perhaps they were sick of his saying wonderful things about himself such as that he existed before Abraham did or maybe they felt he was saying that God gave him the knowledge he had which would be blasphemous if he came across as a know-all.

We must remember that Buddha along with thousands of mystics have also claimed to be I AM. They mean that they found their true identity as a self-existent force that was outside of time and which showed them that time and the body were illusions. They did not all use the term but they meant it. They did not mean that they were having the experience when they were saying such things for it was enough to have had it in the past.

But the simplest answer to the claim that Jesus meant he was God by calling himself I am is that even in Exodus, Yahweh calling himself I AM WHO AM could just mean I am not going to tell you who I am. Or it could mean, If I tell you who I am I will have to tell you what I am and I cannot do that so I just am what I am and that is all I can tell you. Jesus could have meant these things about himself and was indicating nothing more than that he was a mystery like God. This would imply Jesus was more than a man. He would have to be a great angel. Whatever Exodus means by the name or title, Jesus meant something different. In Exodus there is no evidence that the title conveys that God is eternal while Jesus claims to transcend time. In the Catholic book, Set My Exiles Free we are told that I AM WHO I AM means Yahweh and Yahweh is part of the Hebrew verb “to be.” “To be” to the Hebrews would have meant “to be here”. So the name Yahweh means “I am here because I will be with you always” (page 43). This is probably confirmed by verse 12 where God promises to be always with Moses and his people Israel.
 
Jesus says in this chapter that the law is right to demand two independent witnesses before anything can be believed and he says it is true of him and he testifies to himself and so does God. The trouble is we have only his word that God testified so that was silly of Jesus. It also gives anybody who can get two clever and believable witnesses to testify to revelations that some long dead person is God the right to be believed. When the apostles held to such a bad standard we cannot take them or the gospellers too seriously. But enough digression. Jesus argument for two witnesses works best if he is not God. Yes it still fails but it still works best. He said he wanted two beings to witness himself and God so they are two beings for if he is both God and man God cannot be a distinct witness. He indicated in this same chapter, John 8, that the I AM references are not literal declarations of deity.