I've just figured it out. I've been thinking this for some time but tonight's episode of Doctor Who, "The Wedding of River Song," clinched it. I will now explain, however, DOUBLE SPOILER ALERT so click away now if you don't want either Doctor Who or Torment ruined for you. Incidentally, if you haven't played Torment, it is your duty to log onto GOG.com and download it DRM-free for just $9.99 because it's an awesome game.
In the 1999 cult classic video game, Planescape: Torment, you, the protagonist, play a heavily scarred immortal amnesiac who travels across the universe trying to work out exactly who he is. Over the course of the game you find out that he is the nth incarnation of a person who, in his first lifetime, committed a crime so horrifically heinous that not even a lifetime of good deeds could then save him from burning for eternity in the bottomest, foulest pit of Hell. What this crime is is never mentioned in game. So to avoid this, he pledged his life to goodness and also sought out a witch named Ravel Puzzlewell who he had heard could make him immortal. Her price for doing this was that he pose her a riddle that she could not answer - "What can change the nature of a man?" - and she duly made him immortal and to test it, stabbed him in the throat and killed him stone dead. Bingo, it worked, but incorrectly - he couldn't remember a thing. The rest of the game is him trying to figure this out. Whenever he dies, he forgets things, sometimes everything, but wakes right back up.
The answer is, he's The Doctor.
Here's how it works. The Doctor, being a time lord, can regenerate upon dying into a brand new form but only a limit of 12 times. So upon his 13th incarnation, once he dies that's it, it's all over. So upon the end of his life, the 13th Doctor realised that once he died, he would be condemned to an eternity in the foulest pit of Hell because some time either when he was Paul McGann or Christopher Ecclestone, he committed multiple genocide, in that he eradicated in all realities both the time lords and the Daleks, thus bringing the Time War to an end. He then spent the rest of his time as Christopher Ecclestone, David Tennant, Matt Smith, and two other folks trying to save people from horrible monsters and situations and generally being an all round good egg. Unfortunately this is not enough so he navigates the TARDIS through the timey wimey ball and parks up in Sigil, The Planes to find Ravel to make himself immortal so that he won't suffer forever for this. This is not without precedent, as in the (rather execrable and entirely typical of Russell T. Davies) 2010 episode "The End of Time" the Master was resurrected.
It should be mentioned that time lords, when approaching the end of their final lifetime, start to literally decompose alive, as shown in the 1976 episode "The Deadly Assassin" where we see the Master as little more than a grey-skinned walking corpse at the end of his final incarnation. This explains why The Nameless One not only looks nothing like the Doctor but also has grey skin, a smell of death about him, scars on his scars, and walks like both his hips are broken.
Unfortunately it went wrong and he forgot almost everything, including that he was a time lord. Since the time lords are extinct, nobody in the entire multiverse would have cottoned on to the Nameless One being a time lord, and thus could not have told him. He would therefore have no reason to believe he was anything other than a human. However, not everything was forgotten. At the opening of the game Torment, he is woken up on a mortuary slab by a talking skull who knows an awful lot and who reads a map and directions painted on his back. This is a trick that the Doctor first used when he encountered the Silence, who, for the benefit of the uninitiated, are creatures that resemble grey aliens who you forget you've seen immediately you look away from them. He and his companions would draw tally marks on their hands and bodies whenever they saw one so as to assist their memory. No doubt he had this in the back of his mind when he tattooed the map and instructions for future lives on his back.
What clinched this for me, though, was today's episode, "The Wedding of River Song," where the Doctor is trying to avert his own inevitable death and find out why he must die, despite the fact that if he does not die as he is supposed then time will disintegrate and everything will happen at once. There is a sequence where the Doctor consults the still-living dismembered head of a blue-skinned sage, Dorium Maldovar, to find this out. The head is in a box and in a gallery containing large numbers of other living dismembered heads, most of whom have been rotted and reduced to just skulls, who all turn to face the Doctor as he comes into the gallery. This is almost exactly reminiscent of the scene in Torment where the Nameless One rescues his faithful talking skull Morte from an almost identical gallery. Furthermore, in the same scene in Doctor Who, it is shown that the skulls can direct themselves and attack people. Morte, in Torment, gains the ability after this episode to summon a "skull mob" that bounces across the screen and masticates a single target enemy to death. Furthermore, Morte is described as the head of a sage who inadvertantly led the Nameless One to his (original) death by lying. The sage that the Doctor consults claims that there is a question that must not be asked, which is said to be "Doctor Who?" but this is mentioned as the first question. It's entirely possible that there are other forbidden questions, one of which may well be, "what can change the nature of a man?" for instance.
But wait, there's more!
In the game, the Nameless One had a lover in a previous incarnation called Deionarra who was a prophetess and utterly devoted to him and who knew that she would die and be forever separated from him and only appears in the game as a ghost. Near the end of the game it is intimated that she knew his name by virtue of having consulted the bronze sphere (a record of his first incarnation's entire memories). It's not a big stretch for Deionarra to be River Song (the Doctor's lover and now wife, who, in an earlier episode on the 2011 series, was revealed to be part time lord herself by the power of the timey wimey ball), who, by virtue of having met the Doctor in reverse order (I'll explain later, but each time she meets him is in his time stream before the time she meets him after that in her own time stream, basically) knows his personal future and could well therefore fit the definition of a seer or prophetess, at least as far as he is concerned. Furthermore, both River and Deionarra are fond of referring to their men (man?) as "my Love" and speaking in a slightly doom-laden voice.
(Of course, there is a slight problem that River Song was killed in the 2008 series by a swarm of microscopic air-piranhas, given that in Torment it's explicitly mentioned that she and the Nameless One met both as live persons...)
But anyhow, in "The Wedding of River Song," it's quite clear that the Doctor whispers what may well be his real name (never set out in any Who materials) into her ear. So she knows his real name WHICH NOBODY ELSE DOES. The Doctor's penchant for calling himself just "the Doctor" or using an obviously false name coincides with the Nameless One's note to himself to remain nameless because of the power of names and the manner in which one can be tracked down with them. The Doctor admits that he just keeps running and has done for all his life. Coincidence much?
Then there's the fact that both the Doctor and the Nameless One enjoy the company of a sassy Scottish redhead named Annah and Amy Pond respectively. I don't know, maybe Karen Gillan gets a tail by the magic of the timey wimey ball during the Thirteenth Doctor's tenure. Or maybe I just want to see Karen Gillan in that impractically skimpy leather kit that Annah wears in the game. Actually, probably the latter. Let's just pretend this paragraph doesn't exist.
I would also explain how pulling a Zen warrior master named Dak'kon from the remains of a city that's being drowned in pure entropy and taking him with him is exactly the sort of thing that the Doctor would do but I'm starting to stretch things a bit.
Suffice it to say that the Planescape setting in Dungeons & Dragons where Torment takes place is infinite geographically and temporally and as such there are probably corners of the planes where Daleks battle illithids (which are OBVIOUSLY an evil subspecies of Ood - in the 2008 episode "Planet of the Ood" the latter race of tentacle-faces even have an elder brain which co-ordinates all their thoughts and actions) and where Cybermen are recruited into the Blood War as servants of the lawful-evil baatezu. It's therefore also not inconceivable that the Doctor is, for the reasons set out above, the Nameless One.
Now for your thoughts.