Lots of people share their name with someone famous. But how many names belong to two famous people? For example, there have been two famous Richard Burtons and two famous Engelbert Humperdincks and two famous Muhammed Alis. If you want to include fictional characters, there have been two famous Matt Dillons. How many others are there?
(I’m not counting Paris and Perez Hilton, or names followed by “Jr.” or “Sr.” or a numeral.)
Engelbert Humperdinck the singer simply stole the name from the composer Engelbert Humperdinck, in order to make himself stand out a bit a bit from the crowd of other crooners. His real name was Jerry Dorsey, IIRC. I do not think that ought to count.
I rather like the pair of the Romantic poet Samuel Taylor Coleridge and the composer Samuel Coleridge-Taylor (although I very much doubt that this was a mere coincidence either). At one time, when it was free, the online Britannica had them mixed up, so if you searched for the poet you got an article about the composer. (I sent them an email about it, but they did not seem to understand what I was talking about.)
Cassius Marcellus Clay and Cassius (Marcellus) Clay. James Jones and the Rev. Jim Jones. Francis Bacon and Francis Bacon. James Brown and Jim Brown.
Then there are the cases of James Stewart and Stewart Granger, Michael Douglas and Michael Keaton, Davy Jones and David Bowie, wherein the latter changed their names to avoid confusion (not the case with Clay/Ali, presumably).