About the name "Peter" meaning "rock"

[anvi]

Let me throw this out there...

why is Jesus punning in Greek in the first place?

Would this have made any sense at all if this discourse between Peter and Jesus were taking place in conversational Aramaic?

In this case, the Greek pun in the New Testament would have worked the same in the
Hellenized Aramaic that Jesus almost certainly (and exclusively) spoke.  Petros in Greek
is in Aramaic Kephas, which also means "rock."  The New Testament Greek is probably
then a faithful translation of the original Aramaic pun in this instance.  Incidentally, it may
have been Jesus who gave this disciple the name Kephas/Petos, since previously he was
known to his own family only as "Simon" (John 1:42). 

[anvi]

Just one more small clarification, at least as I understand it, from the original post by Supersoulty.  To quote:

"This comes about because the words for “rock” in Greek takes a feminine modifier, while Simon is called what would be the equivalent of “pebble” with the masculine modifier.  Well, this is interesting, except it is simply an accident of language.  In no language, with grammatical gender, would you ever call a man by a feminine verb, and, in fact, Jesus didn’t speak Greek, he spoke Aramaic, and in Aramaic, this sentence would simply be rendered “You are Kephas, and upon this Kephas I will build my Church”… Aramaic has no grammatical gender, so they are the same word."

This is correct.  It's true that "petra" (large rock), which is the direct translation of the Aramaic "kephas," takes a feminine modifier in Greek, and one would never use a feminine modifer for a man's name.  But the New Testament Greek for Peter's name is the masculine form "Petros" (little rock).  In Matthew 16:18, the Greek reads: "You are Peter (Petros), and upon this rock (petra), I will build my church."  The Greek translators modified the form of the name because of the grammatical gender issue.  But we need not worry that the literal distinction between the "little rock" (Petros) and the "large rock" (petra) reflects some distinction in the original Aramaic, because in the original Aramaic Jesus is cited as speaking, the word "Kephas" is used in both occurances (Jesus is not cited as using the Aramaic word "kevna" for "little rock" in either instance of that sentence).  So, the Greek translation is making a slight modification in order to give Peter a masculin name, but the Greek translator in the New Testament is making it, at least as I see it, very clear that the Greek words accurately transmit the original Aramaic meaning of Peter's name.