The "someone" was Davy Jones of the Monkees, who were kind of a big deal in the sixties. It's not that he couldn't use it, but he was unhappy as the name caused confusion.
He actually very briefly went by Tom Jones, to the point of doing a photoshoot under that name, before It's Not Unusual came out and forced him to change it again.
Wow that's some bad luck! At least "Bowie" stuck after that, it's a cool name.