In this question it says Will Smith named his character because, if people were going to remember his character's name then it may as well be the same of his work...
Alfonso remarked that Will had to be careful in naming his character, as people would refer to him in public by that name for the rest of his life, and suggested that he name the character "Will Smith".
I thought that most shows created a character and then sought a cast who could play them. Is it common for cast members to name their own characters?