Mathews 16:16-18

16. Simon Peter answered and said, “You are the Christ, the Son of the living God.”
17. Jesus answered and said to him, Blessed are you, Simon Bar-Jonah, for flesh and blood has not revealed this to you, but My Father who is in heaven.
18. And I also say to you that you are “Peter, and on this rock I will build My church”, and the gates of Hades shall not prevail against it.

Here we have our Lord Jesus Christ confirming Peter did not know Jesus was the Son of God by His physical appearance or moniker, but that it was revealed to him in Spirit, through his strong faith, that He was The Son of God.

Let’s examine carefully Peter’s answer when Jesus asks him who he though He was: “Christ, the Son of the living God”. So first Peter identifies Jesus by His moniker (Christ) followed by His heavenly title: “The Son of God”.

The Lord replies back to him saying “I also say to you”, meaning he was going to respond back to Peter in the exact same manner. And so He did, identifying him first by his other moniker, “Peter”, followed by the spiritual significance of what it represented: “The Rock” on which the Church will be built. The Lord did use Peter’s real name in paragraph 17 (Simon Bar-Jonah), but in paragraph 18 he used his other moniker in order to make the point: to many He was just someone known as “Christ” but few understood that “Christ” meant “The Son of God”. Likewise many knew someone known as “Peter” but few understood that “Peter” meant “The Rock”.

So as we see here, our Lord did not say that the foundation of the Church was a person (known as Peter), but what he represented in the spiritual sense (known as The Rock): the unwavering faith and love for God that helps man get to know the Father as revealed by the Spirit:

“flesh and blood has not revealed this to you, but My Father who is in heaven”

P.S. “Peter” already meant rock as that was the Apostle’s nickname, so there was no need to say “you are Rock, ‘the rock’ on which the Church will be built”, but the Lord simply said “you are Peter, and on this ‘rock’ the Church will be built”. But it is clear the rock in the second part has a different meaning, a spiritual one.