As I understand Dissociative Identity Disorder, new personalities are made when a person, typically a child as they are still very mentally malleable, undergoes extreme duress/trauma. These personalities then tend to come to the forefront when the main person is under stress I think.
For the MC, B1 was probably made when he saw his mother's hanging corpse. At that point, he was hoping for a new, safe, normal life. I am guessing the personality surfaced occasionally throughout his childhood and teenage years, but never for long enough to cause anyone to suspect anything. At least not from what we know, maybe his parents know something and decided it was fine, but can't speculate so far.
B1, being against Skall and wanting to destroy it would make sense as anything related to LL would considered an enemy of both himself and the MC, so getting rid of the people involved would be best.
But that's just me speculating with the info we have so far. That aside, from what I know, the various personalities that are part of DID can be merged together with the main one with therapy and help. They can also be heard in the head of the main personality in some cases as distinct personalities and voices, but I don't know enough about that to say if that may happen here. It doesn't seem to be the variety of DID.