Actually Mishima Reika aka Ayato's Ishitori was not Mishima Haruka. She merely looked like young Haruka, because that was the look of the girl Ayato desired (again, remember Quon and her Ishitori). In the last scene with Mishima, she called herself Haruka, because that was the memory of Ayato's past, and she WAS young Haruka, not Reika.
P.S. I edited the previous post to be a bit more clear (added "Reika" after "Mishima" in 2.)