Unhelpful answer Edit
The answer as originally answered does not apepar to be what the OP asked.
Whether the person who interpreted the question the way that (s)he did likes it or not, the fact remains...
William Hartnell, Patrick Troughton, Jon Pertwee, Colin Baker and Christopher Eccleston were ALL credited on-screen in EVERY episode of their respective eras as "Doctor Who"(or "Dr Who"). David Tennant, in his first appearance, was credited as "Doctor Who". Radio Times listings, promotional material, interviews , including with the actors themselves, have seen them referred to a s"Doctor Who". Colin Baker, Sylvester McCoy and Peter Capaldi have all referred to their character as "Doctor Who" more times than anyone can even begin to count. The Producers etc. from Sydney Newman and Verity lambert, right through the various Barry Letts etc., right down to Russell T. Davies referred to the character as "Doctor Who". Official books refer to the character as "Doctor Who". The list goes on and on.
It is only in the Steven Moffat era that "The Doctor's name is a mystery" or "Basil"(?)
The correct answer to the OP's question is "Tom Baker". 188.8.131.52 15:27, December 16, 2016 (UTC)
His name is not, and has never been, Doctor Who. Steven Moffat in no way came up with the concept of it being a mystery. "An Unearthly Child", "Silver Nemesis", and "The Girl in the Fireplace" are all pre-Moffat stories that refer to the mystery (the latter of those stories was admittedly written by the Moff, but was pre-Moffat-era). Also his name was NEVER canonically Doctor Who, whatever 'official books' say. Also, source on the Doctor's name being Basil? I'm not accusing you of lying/joking/trolling, I genuinely want to know! 184.108.40.206 21:26, December 16, 2016 (UTC)