Part of me wonders if River already knows (or will find out at some point) what this secret is. We still don't know how she learned his name, which she whispered to 10 in the Library.
She's his wife. She probably saw his license when he was pulled over for driving a Tardis under the influence of jelly babies.
Honestly, I just assumed a timey wimey paradox is why the Doctor tells River his name: he knows she has to know it since she told it to him. And that's the only reason he told her. Though I guess, it's just as likely she was there on the Fields of Trenzalore when the Question was asked.
If they do give his name, I hope it is done Neverending Story style- unintelligible to the audience* and giving us something new to debate for the next 50 years. *I know it was Moonchild in the book. But that's neither here nor there.
This is what Tennant's Doctor said to River in Forest of the Dead, "River you know my name. You whispered my name in my ear. There's only one way I would ever tell anyone my name. There's only one time I could." So yeah, its pretty much established unless someone can prove that 10 is lying.
I actually couldn't care less about what his name is. A name is only a sound that is associated with a person. And Moffat can come up with any sound to associate with the Doctor. It's really meaningless. It would only be shocking (to some) if it was something like Jesus. But, they won't be going there. No, I'm much more interested in his backstory. His early days before he ran away from Gallifrey. The circumstances of him stealing the TARDIS (and the TARDIS stealing him). To me, that's WHO the Doctor is, and the answer to the question. Not a name. Mr Awe
The Doctor and River are the only ones in that scene, so he'd either have to have been lying to the one person who would know he was lying, or to himself for the benefit of the audience. Either way, I think we have to take that one at face value.
Wasn't "Rule 1..." a Moffat invention? As much as I enjoy the mans writing, I never did care for that statement. Like the Sonic Screwdriver it seems dreamed up as a "get out of jail free card" if you will.
It depends entirely on the secret and how incredibly cool / breathtakingly stupid it is. I couldn't give a damn what his name is, so if it's something as idiotic as that I'll be...err...quite underwhelmed (to put it ridiculously politely). I hope Moffat will come up with something worthy of all the buildup, because the ongoing "Doctor Who?" thing is becoming rather irritating.
I'm goign to say Yes and No. Yes of course it is interesting to get to know bits about the charcater, but the danager is that if you build it up to much it can't do anything other than dissapoint.
River is a perfect example of that. The wonder of the character in 'Library' was lost over the course of trying to make her cool. Unfortunately, she jumped the shark and became someone I'm happy not to see, in spite of her being performed so well by Alex Kingston and the chemistry she has with Matt Smith.
So "Kilgore Trout" is the name River whispered to him...? If that's true, then Jenny and Vastra being the inspiration for Sherlock Holmes was in fact a fiendishly clever foreshadowing of the Question. ...either that, or you're completely bonkers. Gotta be one or the other.