It's only what's been signposted for the last five years; "River, you know my name... There's only one reason I would ever tell anyone my name. There's only one time I could."
This is Moffat we're talking about, though; the man who said the Doctor who got shot and killed by the Astronaut was DEFINITELY HIM. Well, it was, but not in the way we thought. He's a master of subterfuge and misdirection - he's said the Doctor's greatest secret WILL be revealed, but he hasn't said to whom. He respects the series and its history (despite what some think) and there's no way he'll undermine the whole show by revealing its fundamental mystery. He's been at pains, with the whole Trenzalore/Silence plot, to point out that it MUSTN'T be revealed! If it is, Silence Will Fall (i.e. there'll be no more show)...
He could whisper it to River, who'll look amazed and awed, but the audience won't hear it and nest the Doctor will swear her to tell no one his name. She will say yes, which must be the truth, and we get to keep on wondering 'Doctor Who'. Or some variation there of, so the mystery remains. Whatever, I doubt we'll learn his name.