"Pene" is the Spanish word for the male organ. I don't mean to be obscene, but with the growing number of Spanish-speakers in the US, I think it's useful for parents to know the meaning of this word and avoid any potential for embarassment.
What njc503 said is precisely the reason why I (and my name is Penelope) neither adopt nor respond to this nickname; I'd much rather be called a name that means a coin ("Penny") than... erm... *that*.