That's about as traditional an Italian name as you can get—Lorenzo is an Italian variation on Laurence, which means "laurel wreathed," and it's a name that is currently residing in the top 350 baby names in the U.S. The middle name, Dominic, is actually a much more popular name (currently ranked number 76), and means "belonging to the Lord."
The name flows pretty nicely—though for some reason, I can't stop picturing Brad Pitt and his crew trying to say it in their hilarious faux Italian accents in Inglourious Bastards. The name may be a bit of a mouthful, but it's perfect for a child of two people with strong ties to their Italian roots. And there's nothing more timeless than choosing a name that reflects your family's heritage.
Given the Jersey Shore crew's noted passion for nicknames, though, I'm guessing he's not going to be called Lorenzo on a daily basis. The most common nickname for Lorenzo is simply Renzo, but I'm guessing they're going to be more creative than that. Maybe something like EZ or Enzy or Zo?
What do you think of Snooki's name choice? Would you consider choosing a baby name that reflects your family's heritage?