Old Reggie: Yes
And the fact that "thou art Peter" and "on this rock I will build my Church" are what, random reminder who Jesus was talking to in case St. Peter forgot what his given name was?
Why is it that some people seem to enjoy inane analogies? Did Jesus forget Peter's name when He called him "Simon, son of John" the last time recorded in Scripture? (John 21:15-18)
I suggest you read the Catechism to find the Church Teaching on the relationship between Peter and the Rock upon which the Church was built.
Hint: "This rock" is not Peter.