Interesting tibdit: I went to middle and high school (in Los Alamitos, CA) with Jodie Sweetin, who played Stephanie on the show. She was known around campus to be both a bitch and a hussy, disliked by many.
If I recall correctly, Jessie had changed his name to more of a rock star name. Then there was an episode where his family was involved and he gained a real sense of family pride and then changed his name back to the greek Kosopoulis(sp?)
You may be thinking of The Fresh Prince of Bel Air. On that show's final episode, IIRC, the father considered selling their house to Donald Trump, I believe it was.
Speaking of Jessie's last name, wasn't there an episode where it's revealed that Jessie's real first name is Hermes? Yes, but there was also an episode in one of the last seasons of Full House where some rich guy comes to the house saying he used to live there and offered a lot of money to buy it from them, but they ended up not selling it because Michelle didn't want to move.