I don't know but it has to be amazing, alien sounding and beautiful, but I don't want to know his name it's called doctor who for a reason, he has an air of mystery around him and if we knew his name it would spoil it for lots of people
He seems to like the name John Smith. 1)It was his name as a human. 2)When he thought he was an "almost doctor" (doppelganger) he said "you might as well call me John Smith." 3)When he was trapped in a plane-thingy (in the episode midnight) he told them his name was John Smith. Obviously his name isn't really John Smith and sadly I don't think we'll ever know the answer...
Dr. Infinity, or maybe Dr. ∞ (the infinity symbol itself) since it's almost (or really) impossible/hard to say a symbol, it's hard to say his name. I also think he might become immortal, never run out of live(s)