First and foremost I was able to guess how they planned on having the Doctor survive being killed by River the moment they showed the second clip of the Tesselector in the recap (when the Doctor is heard saying that it's being controlled by miniature people). Rarely is something shown in the recap that doesn't have some impact on the episode itself, and while the first clip with the Tesselector I could contribute to just being part of them confirming that it would be River killing him, the second one made me realize that it was likely going to have a very big impact on the story, far bigger than just supplying the Doctor with information early on the way it did.
As for the question, I think it's in reference to his actual name and not quite just him revealing himself as the Doctor as you suggest it might be Tummie. Since the very first episode of Doctor Who, "An Unearthly Child", there has been an extremely long running "joke" as to who the Doctor really is, and it's been suggested multiple times (especially around the time of the 7th Doctor) that his name wasn't something he just chose to leave behind, but that it is a very dangerous secret that should never be revealed.
-Lady Peinforte in the 7th Doctor episode "Silver Nemesis" revealed that she possibly knew who the Doctor really was, and that he wasn't just another Time Lord (which he himself attested to in the episode "Remembrance of the Daleks").
-In the 10th Doctor episode "A Girl in the Fireplace", Madame de Pompadour, in reading the Doctor's thoughts, suggested that his name was "more than just a secret".
-In the 10th Doctor episode "The Shakespeare Code", the Carrionite Lilith was unable to derive his name with her witchcraft, commenting that "There is no name. Why would a man hide his title in such despair?"
-In the 10th Doctor episode, "The Fires of Pompeii", the one girl given soothsayer powers from inhaling the ash of the Pyroviles commented that Doctor wasn't his real name, and that his real name was hidden under the Cascade of Medusa herself.
I think that it's the Doctor's true name that the Silence fear will be revealed, that it is somehow so terrible a secret that the Doctor must die to prevent it from being revealed