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What is their true form? If you asked the character, and they had full knowledge of themselves, what would they say?

If I understood that correctly, I'd assume you mean we're to create multiple characters for each of them. Otherwise I can only repeat my earlier examples.

Does this include Sonic the Hedgehog and his alternate form Super Sonic?

Well, I don't know what Super Sonic actually is. But as I understand, Super Sonic is "just" powered up form of Sonic (a bit like he has some über-duber armor or weapon), so... no, he doesn't. But if he perceives himself as different person, then it would definitely be, otherwise I don't see any way to categorize him differently than regular sonic. Similarly Breath of Fire games have the main character transforming into some dragon-like entity, yet they're still exactly the "same" as before.

Clark Kent as Super Man's guise would be closer because he separates the two as two different people, even though both are the same truth. This is what the Sarafan Lord example was, but in case of the Sarafan Lord, it's a spoiler, but everyone knows Clark Kent is Super Man. Pretty much means for protagonists this is much more difficult to define.

IIRC, Jean Grey / Phoenix is a good example. They're the completely different people yet many perceive them to be the same in some level.

Seems that "state" was not as clear or good choice to describe what I was looking for, now.

Most obvious cases are when adding the character and you don't know _which_ character class (human, monster, undead, etc.) to use for them because different ones applies depending on different things, like with Arthas, early on he's humanoid, yet later on on the story he's undead (and completely different person with that). But not limited to these.

Wish I had a list of characters we already have to put as examples now.

Edit: Smeagol/Gollum might be another example, Gollum being the completely corrupted form of Smeagol with little or none of the earlier personality left (they're even physically completely different).
Edit2: I feel like I'm contradicting myself with the Super Sonic case, and I can't explain it better than how I already have.
Edit3: Super Sonic could be considered in the way the Disney variations of some characters, but this would make the BoF case also valid for similar treatment.

Samir Duran and Kerrigan from Star Craft belong to these. Though as far as I know, Samir Duran only in the same way as the Sarafan Lord (although he's practically the same way as a turn-coat here and therefore not valid). Kerrigan obviously has Sarah Kerrigan and Infested Kerrigan states, and although the latter retains the memories of the former, the personality is totally different.

Actually Super Man wears Clark Kent as a disguise, opposite from nearly all other superheroes.

Mostly those that want to live a "normal" life have them, like Batman and Spiderman.

CLAMP's characters would especially benefit from this in a way.

The primary purpose would be to maintain character relations in the manner that one character is based or derived from another. This way we can have Aladdin in Disney state that it's based on Aladdin in Arabian Nights. I'm pretty sure everyone knows that Disney doesn't follow the original stories very closely, and therefore using the original characters for them would be "criminal".

This may invite creation of characters that never actually appear in games in their normal form, but only as derivatives, but if there are more than one, there'd then be something to tie them together.

Better wording probably is "variant of", as that would cover characters based on character, derived from character and characters that resemble some character but aren't (and the relation is somehow acknowledged).

Jean-Luc Picard and Locutus of Borg is a good example most should be familiar with.

I'm not saying their isn't such a character that switches states, just that Picard-Locutus isn't it. Now Dax is a much more complicated and likely candidate.

re: re:

Yes, and fortunately all of them have different names with only the Dax part similar :) Don't seem to be many games with Dax though - only one according to screenshots, but they're woefully incomplete source for determining that.

I decided to devote some thought to the Daxes.
The humanoid hosts are easily recognized as individuals. The symbionts are not as easily recognized because they are so different from human individuals that are familiar with. But there is a Dax. It is very complicated. The Dax symbiont can persist without a host and during these times as a complete, albeit relatively helpless, individual. The symbiont eat, grow, reproduce, and communicate in their highly specialized and controlled liquid habitats deep underground. One can assume that they were extremely small in number when they relied on natural processes to maintain their environments (if they even ever existed in such a state, rather than co-evolving with host species, or evolving from a much hardier species in their currently host dependent form, any of which would be consistent with with the Trek universe) Even if the host loses their identity, and even if it is due to brain damage that leaves only the brain stem partially functioning, the symbiont can persist in using the host's body for a short time.
Dax symbiont is an individual that would say they are a symbiont. It has been established that symbionts have very strong identities.
The humanoid hosts are individuals that would say they are humanoids. These humanoids are required to have strong identities as well, to prevent them from being overwhelmed by the symbiont's identity.
Ok, here's the really complicated part,
The joined Trill are individuals that would say they are not their former humanoid selves. They say "he" and "she", 3rd person, like they were any other person besides themselves. They would also not say they are symbionts, again using 3rd person language to talk about "the symbiont I carry". They are a new joined-person of a joined-personality. A joining of a whole person with another whole person to make a third whole person. Not a transformation, the resulting person is more like a child of the symbiont & host, with each contributing parts of themselves to the new individual. but they are not gone, just dormant in their own will. Should they be separated, both personalities will assert themselves in full.

So, I'd say not state changing


Next complicated candidate:
Chris Major from John Varley's Gaea trilogy. He's suffering from an unknown neurological disease that includes schizophrenia in its side effects. Then he starts transforming into a Titanide (a created race of aliens by an alien designer). It is his sincere wish to be a Titanide, not just a human transformed into one. A further complication, is his human son which he only found out about after the titanization process began. I don't remember how it turned out. Oh well, I don't think there's any videogames from the books yet. Their probably will be when they make a movie of them.