In Exodus 3, Moses comes face to face with God in the burning bush, and Moses asks Him what name he should give the Israelites for God. And God tells him, "I AM THAT I AM (YHWH); and He said, You shall say this to the sons of Israel, I AM has sent me to you."
That same name "I Am" is used elsewhere by YHWH in the Old Testament such as in Deuteronomy 32:39, Isaiah 41:4, 43:10, 13, 46:4, 48:12, and 52:6.
So that was YHWH, Moses and Israel around 1600-1500 BC.
When Jesus began His ministry in Israel around 27AD, He came bearing the very same name. But wait. He used it for Himself. Here are some examples:
Matt 14 LITV (Green's Literal Version)
24 But the boat was now in the middle of the sea, tossed by the waves, for the wind was contrary.
25 But in the fourth watch of the night, Jesus went out to them, walking on the sea.
26 And seeing Him walking on the sea, the disciples were troubled, saying, It is a phantom! And they cried out from the fear.
27 But immediately Jesus spoke to them, saying, Be comforted! I AM! Do not fear.
32 And coming into the boat, the wind ceased.
33 And those in the boat came and worshiped Him, saying, Truly, You are the Son of God.
Mark 6 LITV
48 And He saw them being distressed in the rowing, for the wind was contrary to them. And it was about the fourth watch of the night when He came toward them, walking on the sea. And He willed to go by them.
49 But seeing Him walking on the sea, they thought it to be a phantom. And they cried out.
50 For all saw Him, and were troubled. And immediately He spoke to them and said to them, Have courage. I AM! Do not fear.
Mark 14 LITV
60 And standing in the middle, the high priest questioned Jesus, saying, Do you not answer? Nothing? What do these testify against you?
61 But He was silent and answered nothing. Again the high priest questioned Him, and said to Him, Are you the Christ, the Son of the Blessed?
62 And Jesus said, I AM! And you will see the Son of Man sitting off the right hand of power, and coming with the clouds of the heaven. (see Psa. 110:1; Dan. 7:13)
63 And tearing his garments, the high priest said, Why do we still have need of witnesses?
64 You heard the blasphemy. What does it seem to you? And they all adjudged Him liable, even of death.
Luke 22 LITV
66 And when day came, the body of elders of the people, the chief priests and scribes, were gathered. And they led Him away into their sanhedrin, saying,
67 If you are the Christ, tell us. And He said to them, If I tell you, you will in no way believe.
68 And also if I ask, in no way will you answer Me, or let Me go.
69 From now on the Son of Man will be sitting at the right of the power of God. (see Psa. 110:1)
70 And they all said, Then are you the Son of God? And He said to them, You say it, because I AM!
71 And they said, Why do we yet have need of witness? For we ourselves heard it from His mouth.
John 4 LITV
21 Jesus said to her, Woman, believe Me that an hour is coming when you will worship the Father neither in this mountain nor in Jerusalem.
22 You worship what you do not know; we worship what we know, for salvation is of the Jews.
23 But an hour is coming, and now is, when the true worshipers will worship the Father in spirit and in truth. For the Father also seeks such, the ones worshiping Him.
24 God is a spirit, and the ones worshiping Him must worship in spirit and truth.
25 The woman said to Him, I know that Messiah is coming, the One called Christ. When that One comes, He will announce to us all things.
26 Jesus said to her, I AM! the One speaking to you.
John 6 LITV
16 And when it became evening, His disciples went down on the sea.
17 And entering into the boat, they were going across the sea to Capernaum. And darkness had already occurred, and Jesus had not come to them.
18 And the sea was aroused by a great wind blowing.
19 Then having rowed about twenty five or thirty furlongs, they saw Jesus walking on the sea. And He having come near the boat, they were afraid.
20 But He said to them, I AM! Do not fear.
John 8 LITV
24 "Therefore, I said to you that you will die in your sins. For if you do not believe that I AM, you will die in your sins."
57 Then the Jews said to Him, You do not yet have fifty years, and have You seen Abraham?
58 Jesus said to them, Truly, truly, I say to you, Before Abraham came to be, I AM!
59 Because of this, they took up stones that they might throw them on Him. But Jesus was hidden, and went forth out of the temple, going through the midst of them, and so passed by."
John 13 LITV
19 From this time I tell you before it happens, that when it happens you may believe that I AM.
John 18 LITV
4 Then knowing all the things coming upon Him, going forth, Jesus said to them, Whom do you seek?
5 They answered Him, Jesus the Nazarene. Jesus said to them, I AM! And Judas, the one betraying Him, also stood with them.
6 Then when He said to them, I AM, they departed into the rear and fell to the ground.
So there it is. Indisputable, unambiguous proof that Jesus is YHWH in Jesus' own words from each one of the 4 Gospel writers
Jesus explains further about His perfect unity with the Father (caps mine for emphasis):
28 "I give them eternal life, and they will never perish—ever! NO ONE WILL SNATCH THEM OUT OF MY HAND.
29 My Father, who has given them to Me, is greater than all. NO ONE IS ABLE TO SNATCH THEM OUT OF THE FATHER’S HAND.
30 The Father and I are ONE.” John 10
Jesus is the Prophet of Whom all the prophets and the Law spoke. And before Him every knee shall bow and every tongue confess that Jesus Christ is...
Purpose and Meaning of "Ego Eimi" in the Gospel of John In Reference to the Deity of Christ, by Dr. James White
The Old Testament and Jewish Background for the "I AM" Sayings of the Logos – the Lord Jesus Christ, by Anthony Rogers