Matthew places Peter's confession beside one of the Gospel's most famous plays on words: "You are Peter, and upon this rock I will build my church." English preserves the meaning only partially because the connection between the name and the noun is less obvious.
The wordplay gives rhetorical emphasis to Jesus' response to Simon.
The Greek text uses Petros for Peter and petra for rock. Behind the Greek stands the Semitic name Cephas/Kepha, also associated with rock. The linguistic relationship is real even though Christian traditions have differed over the precise theological referent of "this rock."
Language alone does not settle every later ecclesiological debate. It does show that Matthew intends the hearer to notice a connection between Peter's new name and the rock saying that immediately follows.
The wordplay prevents the passage from being read as two unrelated statements. Jesus deliberately links Simon's identity as Peter with the image of the rock and with the building of his assembly.
Recognizing the linguistic connection clarifies the rhetoric while still allowing the larger interpretive questions to be examined from the whole passage rather than being decided by an English spelling difference.