Well, we do say "Peeps," but I once read that his descendants say "Pep-iss" or something on that order.

some discussion of the pronunciation here:
http://www.pepysdiary.com/archive/1660/01/22/

Pronunciation:
I gather that the family today says “Peppis” (two syllables) but that Pepys himself clearly used a one-syllable pronunciation, whether Peeps (the usual pronunciation of his name today) or Pepps or Payps. Here’s the conclusion of the 1893 article (and it would be well to point out that the bit on pronunciation comes at the very end of the long, long page):

“The most probable explanation is that the name in the seventeenth century was either pronounced

Just to clarify: I posted one line above. The rest is courtesy of Richard.

One can almost imagine that if his hair were pink, Pepys might actually look like a chick Peep, particularly with that nose!