I don't know why you are fixated with an entertainer using a stage name. Many, of not most of them do. Charlton Heston's real name was John Charles Carter. You think Lada Gaga is her real name? What about Snoop Dog?
In any case, John Stewart's name is hardly phony and made up. His real name is John Stuart Leibowitz. For his stage name, he dropped his last name to distance himself from his father because of an ugly and strained relationship with him, and changed the spelling of Stuart to Stewart because people kept spelling it that way, anyway.
You want phony and made up? Marion Robert Morrison changed his name to John Wayne.
Jeff Christie was the name Rush Limbaugh used when he was a Top-40 record spinner, before he became a political spinner.