Not quite what you’re looking for, but in the show “Bones”, the character Temperance “Bones” Brennan has written a series of novels in which the protagonist is named Kathy Reichs.
In reality, the show Bones is based on the real life Kathy Reichs’ books about the fictional Temperance Brennan.
On the latest 30 Rock, Elvis Costello is blackmailed into performing in a benefit concert with the line, “Elvis…or shall I say Declan McMannus, international art thief?”
Declan McMannus, of course, being his birth name. Perhaps not the very definition of what the OP is looking for, but close enough to warrant a mention.
Redd Foxx’s real name was John Sanford. His brother was Fred Sanford.
Not sure if this is what you’re looking for but:
This week on 30 Rock, Jack (Alec Baldwin) is trying to strongarm Elvis Costello into playing a benefit concert for him. “All right, let’s cut to the chase…Elvis, or shall I say Declan McManus, international art thief.”
Declan McManus is Elvis Costello’s real name.
This would be relevant if the mayor’s name were William West Anderson.