One of the big hints was during "Journey to the Center of the Tardis", where Clara reads the name of The Doctor. What is most interesting about this was that she seemed rather nonchalant about his name. Whatever his name is, it isn't something that obviously shocked or scared her, she is curious why he wouldn't use it.
But lets take a look at the possibilities:
1. Something we haven't heard before that is somehow extremely pejorative. This is probably a terrible answer. Its a terrible answer not from internal logic to the universe, but from a story point of view. A story should show, not tell, and the drama shouldn't need to be explained to the audience. If, for example, "Tezzelwhorp" is a terrible word in Gallifreyan, and also the name of the Doctor, that is not going to be dramatic to the audience. It would have to be explained why it is so serious that the name "Tezzelwhorp" must never be spoken. So I don't think the answer is going to be a series of weird syllables that has some (informed) terrible meaning.
2. Something from Gallifreyan history. Something from Doctor Who history. Perhaps the Doctor is really Rassilon, Omega, The Other (Doctor Other?), or perhaps his real name is even The Valeyard, or maybe...Davros? Or maybe even something like "Gallifrey" or "TARDIS" or "Harmony". Or something more obscure. This is actually not a bad answer, and would explain why Clara was not impressed by her name. If the Doctor is Rassilon, or Rassilon Jr., it wouldn't mean a lot to her.
I am thinking this might be the answer, but there are two calls against it. First, from a television standpoint, the answer should be dramatic by itself, not because the viewer is familiar with events that happened decades ago. I know plenty of us know who Rassilon or The Valeyard are. But again this is informed drama: someone would have to know the history of Doctor Who to make the connection. That The Doctor's name is dramatic because of something we learned 35 years ago instead of something inherently dramatic is... against some of the rules of normal television. Whether Who is different enough to make this type of error is unknown.
Its also the case that if it turns out that his name is Davros, and he is going to have to become amnesiac and end up on Skaro inventing the Daleks, the show has really boxed itself in.
3. Something that is a normal, if symbolic, word: ths would explain why Clara wasn't excited. Maybe his name is "Time", "Space", "Universe", "Life", "Traveler", or any number of things that would seem normal. Remember, she was genuinely surprised that he didn't use it. It was something to her that seemed rather normal. Of course, the question about this is why is it such a dramatic story? After fifty years, is our big revelation going to be that his name is "Doctor Happiness"? It has to be a word that has some symbolic interest. I wonder if his name actually is "Who"? After all, if the question was in plain sight, maybe the answer was as well. I also suspect it could be "Doctor Moon", and that the Doctor Moon in Silence in the Library is actually The Doctor.
4. Something pejorative that is dramatic. Still a possibility, but less so now. If the Doctor's name was "War", "Genocide", "Murder", etc. ...Clara would have not wondered why he doesn't use it. Although maybe he is really "Doctor Evil", and the TARDIS is what he bought with his One. Million. Dollars.
5. Some meta fanboy bullshit. His name is somehow the reveal that this is all fiction and then playfully references how great we all are as a community, etc. Bleagh. Please no.
6. Caliborn/and or Calliope. When the name of his double is spoken on the Fields of Trenzalore, his double is released and he becomes The Lord of Time Victorious, and starts to destroy the galaxy. ...okay, maybe not.
None of those options make sense. But if I had to guess, my kind of random guesses now are that his name is:
So that being said, what do you think? And also, do you think that the revelation will be worth it? Do you think it will be retconned out in a year or a decade?