When speaking to Moses, God gave his name as I AM. On various occasions Jesus used this name for himself.
Evangelical Christians believe that Jesus is God who came to live on earth as a human. One of the prophecies about Jesus being born described him as ‘the mighty God’:
'Unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counseller, The mighty God, The everlasting Father, The Prince of Peace. Of the increase of his government and peace there shall be no end, upon the throne of David, and upon his kingdom, to order it, and to establish it with judgment and with justice from henceforth even for ever. The zeal of the LORD of hosts will perform this.' (Isaiah 9:6-7)
We can prove that Jesus claimed to be God. Whilst we usually refer to God just as ‘God’, once when God was asked by Moses what His name was, He said ‘My name is I AM.’32 By that He meant that He is eternal – He doesn’t have a beginning or an end, He doesn’t change, He is isn’t constrained by time, He doesn’t have a past or a future – He just IS!
Around 1500 years later when some Jews were challenging Jesus’s authority, Jesus takes the very name of God for himself. He says,
“Truly, truly, I say to you, before Abraham existed, I AM.” 33
The Jews then attempted to kill him for claiming to be God, because they understood exactly what He was saying. Jesus similarly used the name ‘I AM’ for himself on other occasions:
Again the high priest asked him, “Are you the Christ, the Son of the Blessed?” And Jesus said, “I AM, and you will see the Son of Man seated at the right hand of Power, and coming with the clouds of heaven.”
But immediately he spoke to them and said, “Take heart; I AM. Do not be afraid.”
Then Jesus, knowing all that would happen to him, came forward and said to them, “Whom do you seek?” They answered him, “Jesus of Nazareth.” Jesus said to them, “I AM.”... When Jesus said to them, “I AM,” they drew back and fell to the ground.
So Jesus clearly seemed to be using the Divine name for himself especially when people were querying his authority and status.
Here is the full passage of Moses at the burning bush.
Moses at the Burning Bush
Now Moses was tending the flock of Jethro his father-in-law, the priest of Midian. And he led the flock to the back of the desert, and came to Horeb, the mountain of God. And the Angel of the Lord appeared to him in a flame of fire from the midst of a bush. So he looked, and behold, the bush was burning with fire, but the bush was not consumed. Then Moses said, “I will now turn aside and see this great sight, why the bush does not burn.”
So when the Lord saw that he turned aside to look, God called to him from the midst of the bush and said, “Moses, Moses!”
And he said, “Here I am.”
Then He said, “Do not draw near this place. Take your sandals off your feet, for the place where you stand is holy ground.” Moreover He said, “I am the God of your father—the God of Abraham, the God of Isaac, and the God of Jacob.” And Moses hid his face, for he was afraid to look upon God.
And the Lord said: “I have surely seen the oppression of My people who are in Egypt, and have heard their cry because of their taskmasters, for I know their sorrows. So I have come down to deliver them out of the hand of the Egyptians, and to bring them up from that land to a good and large land, to a land flowing with milk and honey, to the place of the Canaanites and the Hittites and the Amorites and the Perizzites and the Hivites and the Jebusites. Now therefore, behold, the cry of the children of Israel has come to Me, and I have also seen the oppression with which the Egyptians oppress them. Come now, therefore, and I will send you to Pharaoh that you may bring My people, the children of Israel, out of Egypt.”
But Moses said to God, “Who am I that I should go to Pharaoh, and that I should bring the children of Israel out of Egypt?”
So He said, “I will certainly be with you. And this shall be a sign to you that I have sent you: When you have brought the people out of Egypt, you shall serve God on this mountain.”
Then Moses said to God, “Indeed, when I come to the children of Israel and say to them, ‘The God of your fathers has sent me to you,’ and they say to me, ‘What is His name?’ what shall I say to them?”
And God said to Moses, “I AM WHO I AM.” And He said, “Thus you shall say to the children of Israel, ‘I AM has sent me to you.’ ” Moreover God said to Moses, “Thus you shall say to the children of Israel: ‘The Lord God of your fathers, the God of Abraham, the God of Isaac, and the God of Jacob, has sent me to you. This is My name forever, and this is My memorial to all generations.’