umm i could try.. note that i am basing this on memory and i am not by any means an expert in like brain things and am not tryna be 🥹✌🏾
so anyway, the strongest idea i have is that Diavolo is the OG (or i guess. the host?) of the body, and Doppio comes later.
the main idea that i have for this is that something like super traumatic, probably something really personal, happened around the time he was just entering his teen years? because to me there's genuinely NO REASON for him to be so crazy about being anonymous and erasing any and all traces of his presence SO suddenly.
it seems like someone knowing about him triggers a fight/flight response. like generally, he's kind of chill; he literally only crashes out when someone finds out or is close to finding out his identity. remember how he packed up sorbet and shipped his remains to that group he was from?
so then, he spirals and becomes this weird, antisocial, head-up-his-own-ass freak (having a nearly all-powerful stand doesn't help his case at all). as he does, the more boy-ish part of himself separated from him and became his own person, giving us Vinegar Doppio. i'm not saying Doppio is the teen alter of Diavolo, just generally behaves and kind of looks more akin to a teenager compared to him (more cowardly, has an air of "innocence", usually polite, that stupid fucking swirly "goody-two-shoes" ass haircut of his [/silly], prone to hissyfits, etc).
i think these traits of Doppio are what make Diavolo talk so fondly and gently to him over the "phone". not just because they share the same body, and not necessarily because he's childlike, but because he retains the personality of his younger self. it makes him feel somewhat maternal.
anyways. the reason i think Doppio was even conceived to begin with is to help give his body some rest when needed. i'm not trying to insinuate that Diavolo is angry and tired all the time, but he must certainly be mentally tired. he was anxious on a consistent basis, he had to be; he had to put up and maintain so many walls so that subordinates didn't find out who he is. one slip-up and all those dominoes he spent so much time perfectly spacing could all fall down.
that is when babygirl Doppio comes in ^_^ Doppio could walk around in the open and nobody would know that Diavolo is technically right there, saving him the trouble of having to worry about people finding him out, even if it's for a few moments. he could take a cat nap or something idk