Seems to me there are two views, either Christ named Simon Peter in the incident recorded in Matthew 16 - or Simon was already known as Peter and Christ used that other name to emphasize His point in Matthew 16.
I have no leaning in the Spirit either way on that point but strongly on the point that God is the Rock (Deu 32:1-4) - and Peter is more like Abraham in the construction of the body of believers, both Christian and Jew. Which is to say, first rocks in their confessions - and both called by Almighty God.
Interestingly, the Catechism Of The Catholic Church teaches that it was Peter's confession of faith which was/is the rock.
424 Moved by the grace of the Holy Spirit and drawn by the Father, we believe in Jesus and confess: 'You are the Christ, the Son of the living God. On the rock of this faith confessed by St. Peter, Christ built his Church.
Indeed! That's a great way to put it: "cornerstone" rocks in the true "Rock" which is God.
I regret that your comments on the "specially-announced Name of God--the Rock" got kinda lost in the shuffle here. I'll go back and read your posts on that.