I'll make this simple! Well, I need to use the Greek, but you can look it up anywhere.
In the New Testament, Jesus called himself "I am" in Greek. Eight times alone in the book of John.
This is VERY important! In Greek, there are two ways to say "I am." One is just to use the Present Indicative Active Verb, first person singular εἰμι (aemi). Greek does not usually use the pronoun "I" but does, especially in this case.
In the above passages, and elsewhere when Jesus speaks of himself, he uses both the pronoun and the verb ἐγώ εἰμι (ego aemi) which is "I, I am." So it uses the 1st person singular pronoun, "ego."
So what is the big deal about this? Well, the Septuagint or LXX, is the Greek version of the Old Testament. The Old Testament was translated into Greek around 300 BC, because the Jews were losing their Hebrew language after being taken into captivity in 586 BC by the Babylonians, plus the successful push by Alexander the Great to Hellenize the world.
While there are small differences between the Masoretic Hebrew and the LXX sometimes, they both totally agree on this point. God, or YHWH in the Hebrew, was translated into Greek as ἐγώ εἰμι, which is what Jesus said he was "I, I am."
So in the following passage, when Moses asked God about who he was to tell the Hebrew people who he was, God said:
"God said to Moses, “I am who I am.” And he said, “Say this to the people of Israel, ‘I am has sent me to you.’” Exodus 3:14
So the Jews, 300 years before Jesus, translated YHWH as "I, I am" in Greek and used it as the sacred name of God. In fact, this name was considered sacred by the Hebrew Jews, and was not to be spoken by them. They began to call God, "Adoni" for fear of committing blasphemy by using the sacred name of God.
So, Jesus calls himself "I, I am" in front of the Pharisees, who were determined to keep every law with respect to respect God and to be saved. They were outraged! Especially because he did it over and over, along with making himself equal with God, and saying he was one with the Father. In fact, these were the turning points in which the Pharisees began to plot to kill Jesus.
Conclusion: Jesus called himself the same name in Greek in the New Testament, that was used of YHWH in the Old Testament. "I, I am!"
For further reading on this, click on this link:
http://www.icr.org/article/i-ams-christ/
(And yes, I have studied New Testament Greek in Seminary and just finished my first semester of Intermediate Greek, so I have read this for myself in the Greek, and in Hebrew in the OT because I have also studied and read Hebrew. Not to brag, of course but just to let you know his was not something I picked up on the Internet! )