Shows like George Lopez or Bill Cosby use the real name to attract the viewer. The main character has already a good reputation and a fan base and they want to draw those viewers in immediately.
The same would go for Raven, as she was known before and I guess they just wanted her to be easier to be identified (since obviously she didn't look like little Olivia anymore, but has recognizable face)
As for Miley Cyrus, I am sure they cut a deal that "Miley" was used for the character, as originally the name would have been "Chloe Steward", so Miley would be more in the spotlight and if someone would talk about the show, they would immediately talk about Miley - thus keeping her name in everyone mouth and not the characters one...
As for Lizzie McGuire and Wizards oWP, Selena Gomez and Hilary Duff were not famous beforehand and did not have a name that was "worth something" at that time (e.g. Billy Ray Cyrus would be a name you wouldn't mind to be connected with your teeny show...)
So I hope that helped you...