Well considering my lack of knowledge on the matter(I watched moon knight) the second personality is a trauma response, spawned to help categorizes the trauma to better handle it, or avoid it
so I say the asshole is the original personality, originally I was gonna say the other way around and it's hard to make a guess with little info, but I was going off the assumption the asshole being the split that she only coming out in dangerous situations to protect her, there's a form of protectiveness, like she's shielding her from the world... But then I flipped it, she rarely comes out, traumatic event makes one more isolated, the other personality is cheerful at times, it kinda clicked and I forgot my other reasoning.... But yeah that's where I stand for now, in case it's revealed next chapter
That plan working out for ya chief?