(warning: I am not a lawyer)
The pizzeria most likely has a registered trademark for its name. To use their name (and/or logo or anything else trademarked) you'd either need their permission, or have your usage qualify as "fair use". A quick google search brought up
this article on fair use you may want to read. Also the US Patent and Trademark Office has a good article and video you may find
helpful here.
If I were you I'd try to contact the owner of the pizzeria to see if they will give you written permission. After all, free advertising is always a good thing so they might not have a problem with it. If they don't, you could still probably continue with fair use, although you'd probably want to consult an actual lawyer at this point.
Worst case, you can make up a fictional pizzeria. And who knows? Maybe the game picks up enough steam that your fictional pizzeria will get famous and you'll be able to start your own pizza business!