Disassociative Identity Disorder was written off by the APA for a long time. As I understand, it was recently recognized again.
It’s possible that she’s legitimately experiencing that. More likely that she is convinced that she is, I guess.
Either way, she has issues she is dealing with (poorly or well being up to perspective, I guess).
The real question is:
Are you being harmed by this type of relationship?
Even if just emotional/intellectual, a destructive person is just that.
Or
Do you have something good to offer and get something good in return?
Bonus wordplay fun:
In the Navy, a “headmate” is a person you share a bathroom (called a “head” universally in the Navy) but not a bedroom with. Some barracks rooms had a pair of rooms that shared one bathroom.