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Interestingly, both Abraham and Peter were "first called" and their names were both changed and they were both called "rock" which is a specially published Name of God in the Song of Moses.
– Matt 16:17-18
– Isaiah 51:1-2
– Deu 32:1-4
And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them: and that Rock was Christ. – 1 Cor 10:1-4
– Rev 15:2-4

God's Name is I AM.

Peter's name was changed to a diminutive derivative of the NAME "Rock", a NAME of YHvH.
Abram's name was added to with the breath of Elohim in the form of the Hebrew letter "Hey"
The letter "Hey" is known by the Rabbis as the breath of Elohim.
Both Abram and Sarai had their names changed with the Breath of Elohim in Genesis 17.
"Hey" as a suffix in Hebrew feminizes a name and allows it to be fruitful.
"Hey" is formed from Dalet and Yod, it can be a picture of returning to Elohim
by the transforming power of the "Spirit"
Dalet stands for brokenness and "Yod" stands for a hand.
Opening the door to the heart is a picture of Elohim's indwelling the believer.
I do not find Abraham named the Rock.

NAU Exodus 3:14 God said to Moses, "I AM WHO I AM";
and He said, "Thus you shall say to the sons of Israel,
'I AM has sent me to you.'"
"I AM is the first person singular of the the verb "to be"
To be used by YHvH himself only.
We on the other hand say HE IS or YHvH.
YHvH is the third person masculine singular of the same verb "to be"
Because of man-made traditions,
we have been blinded to the NAME YHvH;
it has been replaced in English with Lord or LORD
It is printed in the Hebrew text but Rabbinical Judaism
speaks the word Adonai as a spoken replacement for "HE IS" or YHvH.
The NAME of Elohim "YHvH" occurs somewhere between
6000 and 7000 times in the Hebrew text.

shalom b'SHEM Yah'shua HaMashiach

Thank you for sharing your insights, dear Uri’el-2012!

"I AM is the first person singular of the the verb "to be" To be used by YHvH himself only.

I frequently say "God's Name is I AM" to share my joy and declare Him:

And when Abram was ninety years old and nine, the LORD appeared to Abram, and said unto him, I [am] the Almighty God [El Shaddai]; walk before me, and be thou perfect. - Genesis 17:1

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. – Exodus 3:14

Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am. - John 8:58

As soon then as he had said unto them, I am [he], they went backward, and fell to the ground. – John 18:6

Remember the former things of old: for I [am] God, and [there is] none else; [I am] God, and [there is] none like me, Declaring the end from the beginning, and from ancient times [the things] that are not [yet] done, saying, My counsel shall stand, and I will do all my pleasure: - Isaiah 46:9-10

I am Alpha and Omega, the beginning and the ending, saith the Lord, which is, and which was, and which is to come, the Almighty. - Revelation 1:8

His Name comes alive to me in the above passages even when it is only implied (e.g. Gen 17:1) - but I do not expect everyone else to see what I see. On the other hand, I cannot contain my joy so I must declare Him.

His Name I AM answers all my deep questions about this life: Why does..." When will...? What are..."

I do not find Abraham named the Rock.

I see Abraham being called "rock" in the first passage below much like Peter is called "rock" in the second, i.e. they were firsts to be called of God:

Hearken to me, ye that follow after righteousness, ye that seek the LORD: look unto the rock [whence] ye are hewn, and to the hole of the pit [whence] ye are digged. Look unto Abraham your father, and unto Sarah [that] bare you: for I called him alone, and blessed him, and increased him. – Isaiah 51:1-2

And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed [it] unto thee, but my Father which is in heaven. And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. – Matt 16:17-18

But again, I do not expect everyone to see what I see.

To God be the glory, not man, never man.