Y'all it's not split personality or multiple personality, it's DID (Disassociative Idenity Disorder). The personalites have their own memories and uniqueness, they don't often interact unless the original primary (Hajime) calls them together. The reason why Rei was born was because Ichigo killed off Hajime, though in theory because it's DID Ichigo should have been the one remaining but I wonder if she killed herself as well. That is what wiped the slate clean and allowed Rei to exist, a brand new primary with no trauma and no alters. I kept expecting Ichgo to resurface especially when the psycho doctor showed up, but I'm thinking that Rei received personalite traits from both Hajime and Ichigo.
She fell in love with her Sensei without it being about sexual touch. (Hajime softening Ichigo's desires)
She still wanted to be a doctor. (This is directly from Hajime)
She found the will to stand up to one of her abusers. (Ichigo 100% ;P)
I have a theory that psycho doctor was the one that created Ichigo in the first place, so it was poetic that it was her personality trait that let Rei knock her on her ass. The end was a little eh to me, I wanted to see at least one wholesome kiss as the final conclusion but going on the picnic again was okay.