Why did Jesus change Peter's name, according to non-Catholic theology?

I have been discussing Matthew 16:18 for years now with both Catholics and non-Catholics. This verse is obviously a very important verse concerning the doctrine of the Bishop of Rome being Supreme Pontiff. The non-Catholic argument that I come up against time and time again is the "play on words" interpretation summed up pretty well here . I understand that, according to this interpretation, Jesus calls himself "big rock," and calls Peter "small rock." > Looking up the original Greek I see that Jesus is referring to two > types of rocks and one is related to the other, but they are not the > same. > > Peter = Πέτρος, Pétros (a masculine noun) – properly, a stone > (pebble), such as a small rock found along a pathway. > > Rock = pétra (a feminine noun) – "a mass of connected rock” The accepted answer goes on to say... > This revelation, being from God, is infallible, and if the Church is > built upon it, it can never fall. Simon was named petros because he > was the **archetype**, the first (of his contemporaries at least) to have > received this personal revelation from God. I've also heard other interpretations that place the "Rock-ness," if you will, on Peter's faith. The answer above labels Peter as an "archetype" for those *individuals* with faith, or those *individuals* who receive infallible revelations. I think this reads to much into it when considering the context of scripture, and is perhaps a presupposition. Obviously Catholics believe that Christ, by changing Simon's name to Peter, established a foundational office of headship upon which the "Keys to the Kingdom of God" rests until his return. Catholics believe that *that* change signified a newly established office, and is *why* Christ changed Simon the fisherman to Peter the fisher of men to begin with. > "The keys of the kingdom" > > 551 From the beginning of his public life Jesus chose certain men, > twelve in number, to be with him and to participate in his mission.280 > He gives the Twelve a share in his authority and 'sent them out to > preach the kingdom of God and to heal."They remain associated for > ever with Christ's kingdom, for through them he directs the Church: > >> As my Father appointed a kingdom for me, so do I appoint for you that >> you may eat and drink at my table in my kingdom, and sit on thrones >> judging the twelve tribes of Israel. > > 552 Simon Peter holds the first place in the college of the Twelve; > Jesus entrusted a unique mission to him. Through a revelation from the > Father, Peter had confessed: "You are the Christ, the Son of the > living God." Our Lord then declared to him: "You are Peter, and on > this rock I will build my Church, and the gates of Hades will not > prevail against it."Christ, the "living Stone",thus assures > his Church, built on Peter, of victory over the powers of death. > Because of the faith he confessed Peter will remain the unshakable > rock of the Church. His mission will be to keep this faith from every > lapse and to strengthen his brothers in it. > > 553 Jesus entrusted a specific authority to Peter: "I will give you > the keys of the kingdom of heaven, and whatever you bind on earth > shall be bound in heaven, and whatever you loose on earth shall be > loosed in heaven."The "power of the keys" designates authority to > govern the house of God, which is the Church. Jesus, the Good > Shepherd, confirmed this mandate after his Resurrection: "Feed my > sheep."The power to "bind and loose" connotes the authority to > absolve sins, to pronounce doctrinal judgements, and to make > disciplinary decisions in the Church. Jesus entrusted this authority > to the Church through the ministry of the apostles and in > particular through the ministry of Peter, the only one to whom he > specifically entrusted the keys of the kingdom. (*CCC 551-553*) My question is, from a non-Catholic point of view, why did Jesus choose "Rock" as a name for Peter in the first place? Answering whether or not Peter is called big rock or little rock doesn't answer why Jesus called him a rock - of any size. I'm wanting to know *why* exactly non-Catholics believe Christ changed Peter's name (rock...big or small), and what does it signify in comparison to what the Catholic Church teaches .