Charles's last name is never mentioned. In fact, at times the writers had to go out of their way to avoid mentioning his, or his mother's surname. This lead people to think that Scott Baio was once again playing the role of Charles Arcola aka "Chachi" from Happy Days (1974) and Joanie Loves Chachi (1982). Ellen Travolta, played Scott Baio's mother on all three series. On Charles in Charge (1984) her name was Lillian and on the previous two series she was Louisa Arcola-Delvecchio.
In the episode "Bottle Baby" (season 3 episode 9), it is revealed that Buddy's proper name is Budence, his sister is named Bunence, and their parents are named Florence and Clarence. A later episode also makes reference to him having an Uncle Laurence.