This is an in-depth rundown of Riya for my reference and so everyone can see what they're dealing with. No, I haven't been looking for a place to bounce him around in. What makes you think that?
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On Nomenclature: Black and White is the name that the author came up with and Atsushi later developed to tell them apart. White is the reserved violinist, and Black is the spoiled cat.
On Switching: Switching is tricky with Riya. Sometimes, he'll do it right while talking to someone with little notice or he will outright collapse. The transitions get smoother as canon goes on, but if you put either side under extreme duress, they're likely to switch off. On this note, neither side can exert a lot of control of when they're going to switch. If one of them wants to retreat, they can, but they can't take control if the other personality doesn't want to leave.
On Telling Them Apart: IC - It isn't difficult to tell the sides apart, but many people in canon have problems with it. (Riya's classmates know he's a bit touched in the head, but have never guessed MPD despite having seen Black before.) Black has very loose and defensive body language, wears simple outfits, has poor motor function (sloppy eating, tying ties, etc.), and speaks using the ore-pronoun. He tends to fuss up White's clothing if he can't change. White is refined and close with his body language, wears formal clothing, has excellent motor function (playing the violin), and speaks using the boku-pronoun. It's at your discretion how quick your characters pick up what's going on.
OOC White has grey border icons with o; prefacing all of his keywords. Black has black border icons with x; prefacing all of his keywords. Black also speaks in a lot of slang, so he tends to chop the ending off words, like running to runnin' and so on. He sounds like a rude child while White sounds age-appropriate with manner.
On Black and White's Relationship: Black likes to lie. Before he was aware of White, he said he had a twin brother as an excuse for why he acts differently. Then he later says he's dead. He weaves lies to defend himself, trying to exist separately which is where the lies about being a prostitute start. Black prefers to keep people guessing, but it's all posturing for the most part. Meanthewhile, White would try to hide what was going on from everyone and refused to go to his counseling appointments. It works out easily enough for him, because he lived alone.
However, Black is aware of White and has access to White's memories now. He considers himself the dominant personality and tries to incriminate White to those around him. White is aware of Black's going-ons to a degree, but has no interest in Black himself. He prefers to ignore what is happening to himself and suppress Black which leads to panic attacks when he's been out of control for a long time. So, the two do not have a good, functioning relationship and will likely be making barbs/comments at each other, privately and with other people.
On Possession: Black is the one who implemented the who belongs to which side system. Once he figures out that someone belongs to White, and he can tell when they're "cheating" on him, he won't want anything to do with that person. If you ever want to know who your character belongs to, just ask. White is not as picky, since he doesn't really recall anyone Black connects with unless someone makes a point to get to know him as well.
You can pick up the canon
here with the other chapters
here or at your bookstore. I'd recommend buying it for the art, seriously.