Some artist who got their peerage from QE are using pseudonyms. So is Sir Elton really Sir Elton, or Sir Reginald? And how about Cliff Richard? Sir Cliff or Sir Harry? I doubt Bobo will get a Sir, but would he be Sir Bono or Sir Paul? And is Geldof Sir Bob or Sir Robert?
I think it’s up to the knightee. According to the IMDb, Michael Caine was knighted under his real name (Maurice Mickelwhite). On the other hand it says he goes by Sir Michael Caine. Elton John is Sir Elton, either for that reason, or because he legally changed his name to Elton John, or both.
I think Marley23 has the right of it. While there are “official” modes of address, it’s all really just a matter of custom and usage. By and large, people choose how they prefer to be addressed, and other people respect that.
On the matter of Bob Geldof, though, as an Irish citizen his knighthood is honorary, and therefore he can’t be “officially” called “Sir” anything (the same would apply to Bono).
Unofficially, you can call him what you like.