He's not renaming Simon in Matthew 4:18. That's the evangelist talking, and he's writing to Christians a few years after the resurrection who knew exactly who "Simon called Peter" was. Matthew designates him "Simon called Peter" in 4:18 to distinguish him from other men named "Simon," in particular Simon the zealot party member.
John 1:
[42] He brought him to Jesus. Jesus looked at him, and said, "So you are Simon the son of John? You shall be called Cephas" (which means Peter).
I imagine it's also possible that Jesus took the "Rockyness" away from Peter the last time, recorded in Scripture, He spoke to him.
John 21:
[15] When they had finished breakfast, Jesus said to Simon Peter, "Simon, son of John, do you love me more than these?" He said to him, "Yes, Lord; you know that I love you." He said to him, "Feed my lambs."
[16] A second time he said to him, "Simon, son of John, do you love me?" He said to him, "Yes, Lord; you know that I love you." He said to him, "Tend my sheep
." [17] He said to him the third time, "Simon, son of John, do you love me?" Peter was grieved because he said to him the third time, "Do you love me?" And he said to him, "Lord, you know everything; you know that I love you." Jesus said to him, "Feed my sheep.