I would guess that "Pauly" is an obvious pet name for "Paul" or (for a girl) "Pauline". If you check out this link to this website
http://behindthename.com/p.html
you'll find that "Paul" means "small" or "humble", along with some additional information on some famous Pauls.
Of course, if you've just seen the movie "Pauly" about the wise-cracking parrot, then I would say that "Pauly" is a play on words for the traditional parrot name of "Polly". But, of course, "Polly" is a girl's name, and I suspect that the mucho macho parrot of that movie must've gotten his feathers somewhat ruffled over being called "Polly". So the producers wisely advised the screen-writer to change the parrot's name to "Pauly".
"Pauly" is also the name of one of the mafioso characters in the current hit HBO teevee series, *The Sopranos*, but I think if anyone were to offer that particular Pauly a cracker, he'd probably crack a few heads.
-- Nanaea