Simon, son of John, we know him better as Peter (Cephas) and he is a favorite character in the Bible and one that shows “God-growth” from the beginning to the end of his story. A meaning of Simon comes from the word for “hearing” and John means “Jehovah-favored” and this may all come from a word that means, “dove” and it is a possible form of Jonah (some Bible translations will use Jonah instead of John). (Those “Jonah” people and fish, boats and water, sounds like another Bible study to me.) Cephas or Peter means a “piece of rock” or small pebble.
Matthew 16:18 is a verse that I think needs to be looked at a little different. Why would Jesus say that Peter, a “small piece of rock”, would have the church built on him when he used a term for a “large rock” in the same passage? Lets try it this way; Jesus points at Peter and says he is a “part of the rock” and then gestures towards himself and says but on the “big rock (Jesus)” will the Church be built.
Resources: The New Strong’s Exhaustive Concordance of the Bible, my brother Luther