He didn't. He named him Cephas, which means 'building stone'... A hand-sized stone used as part of a wall. Different from a foundation stone or cornerstone.
Baptist scholar D. A. Carson, writes, in The Expositor’s Bible Commentary:
[T]he underlying Aramaic is in this case unquestionable; and most probably kepha was used in both clauses (”you are kepha” and “on this kepha”), since the word was used both for a name and for a “rock.” The Peshitta (written in Syriac, a language cognate with a dialect of Aramaic) makes no distinction between the words in the two clauses.
This claim that the word “petra” or “cephas” means “little stone” is a complete fiction. Peter is called “Petros” because he is a MALE; the word “petra” is used in the next phrase because the word itself is feminine. There is NO difference in meaning.
There are several other points that make it clear that the “linguistic” arguments that Jesus intended to distinguish between Peter the man and the “rock” on which he would build His Church, are desperate fabrications.
http://catholicnick.blogspot.com/2013/04/why-protestant-petrospetra-argument-is.html