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Thank you for sharing your insights, dear sister in Christ!

Concerning Peter being called "rock" I would also point to Abraham being called "rock" - both of them being the first to believe, Judaic on the first hand and Christian on the latter:

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 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 16:18

God's Name is I AM.