Without ever wanting it, the Doctor has become an icon; there are even statues of him on various planets, where he’s lauded as their saviour, all because he leant a hand at a tricky moment in their history. It’s one of the downsides of being a compulsive busybody, so it’s fortunate that his face changes periodically. It keeps him from being recognised too often.
His name is widely known though, and not everyone is a fan. There are whole worlds where his presence is less than welcome.
He never planned on becoming famous; he just has to live with it.