Furthermore, puns in other languages are not unheard of. Consider:
That's a pun in Greek and you probably had it explained to you as a child. There's no need to be able to speak Greek to understand that "Peter" means "rock".
Compare this with John 1:42 "You are Simon the son of John. You shall be called Cephas” (which means Peter)"
The Geneva Study Bible says that in Matthew 16:18 Jesus would have used the word Cephas, the Aramaic form of Peter. Paul also refers to Peter as Cephas.
Hebrewgospels.com, in their translation of the Hebrew manuscript of Matthew which they claim derives from the original Hebrew Matthew, add a note at 4:18. The verse reads, "And it happened when Yeshua went to the sea of Gelilah, that he saw two brothers - and they were: Shimon who is called Keipha..."
The note says, "[Keipha is] the Aramaic name for 'Peter', Greek transliteration 'Cephas'. A number of Aramaic nouns were used post-exilic Hebrew."
So if the Aramaic word Keipha was used in Hebrew at that time, the pun you quoted from Matthew 16:18 makes sense if it was composed in Hebrew, with Peter's name in Aramaic.