Basically, at the end, there were these two tightly bound souls, or minds or essences, one of which was dying, and between them, they had two bodies, one of which was badly wounded and possibly dying, and the other of which was hale and hearty, and so the intact soul/life force/brain that still had reasons to live moved into the more viable body, and the one that wanted to die and maybe pass into oblivion took the body that would let him do that. That's how I took the meaning of Min's viewing of Rand merging with another man, as well as Rand/LTT's perception that Moridin was a part of him/them, and the spillover thoughts.