"Pizza dude" is the most common name for the pizza delivery guy, who indeed usually does have a peice of crap car. Can also mean, although used less commonly, the entire pizza place itself.
yooo Josh gimme 10 bucks, the pizza dudes here
man, i'm hungry, call the pizza dude
Pizza delivery person, usually seen driving a hoopty. From the '80's Tom Hanks movie "The 'Burbs", where Corey Feldman implores his friends not to leave, it is worthwhile to hang around, because the Pizza Dude is coming.
"Get ready to answer the door, I hear the Pizza Dude's hoopty coming up the block."