No, actually I believe he was talking to Peter. So your assumption is wrong. Christ did not, in that passage, give all authority to Peter to be *the* apostle. That is emphatically wrong. Christ names Peter “cephas” because of his character traits and that is what Christ built the Church on. Unwavering truth like a rock!
“You are ‘Rock’, and upon your rockly character traits I will build my church. For about a hundred years. Then read the book.”
“Unwavering truth like a rock!”
He did deny Christ three times after that.
Not to insult Peter; I know Jesus forgave him.
But, you know, not exactly unwavering truth like a rock.
“...and upon this rock I will build my church, and the gates of hell shall not prevail against it. Whatsoever you bind on earth shall be bound in Heaven, and whatsoever you lose on earth, shall be losed in Heaven.”
What part of that don’t you understand?
The name change transcends merely ascribing “characteristics” to Peter. Peter was given the keys to the kingdom. Like all previous name changes,Abram to Abraham, real, tangible authority accompanied the name change.