Peter was just a small stone built atop the bedrock of something much bigger than himself: namely,
the truth that Jesus is the Christ the Son of the living God. Put simply, Peter was not the rock; Christ is the Rock.
It's not unusual for God/Jesus to change a persons name ... biblically a person's name describes their character ... and when a change in character happens the Lord see's fit often to give them a new name that describes their new character (new identity). ie Abram/Abraham, Sarai,/Sarah,
Jacob/Israel (many others)
When several people in the Old and New Testament had a spiritual awakening by coming to God, on a new or deeper level, He gave them a new name,
a new identity that redefined their lives. No longer would they be defined by their old ways but rather be called and realized by their new names/new character.
John 1:42
Andrew brought him to Jesus, who looked at him and said, "You are Simon son of John. You will be called Cephas" (which is translated as Peter).
Simon had a spiritual awakening/revelation .... as Jesus stated .... ie ... My Father has revealed this to you ....
Matthew 16:17
King James Bible
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.
The church (body of believers) is built on Jesus (who was without sin) ... Peter was a sinner. (ALL have fallen short)
1 Corinthians 12:13). Anyone who believes is part of the body of Christ and has received the Spirit of Christ as evidence. All those who have received salvation through faith in Jesus Christ comprise His church (body of believers).