What about Maurice Micklewhite?
I stumbled across this TVC by accident. It was Norwich Union renaming itself Aviva late last year, and features Bruce Willis, Elle Macpherson, Alice Cooper and Ringo Starr. The idea was that each of these celebrities changed their name before they became famous.
I am not sure if the first two qualify: the first was born Walter Bruce Willis and from what I can tell, was just known as Bruce. I’ve a few friends in the same boat, where their families called them by their middle names. Elle Macpherson might have been Eleanor Gow, but Elle is a reasonable shortening of Eleanor, and Macpherson was her stepfather’s surname.
Alice Cooper was indeed Vincent Furnier and Ringo Starr was Richard Starkey.
I imagine Elton John, Cliff Richard and Michael Caine weren’t available.