They are who they were in prior lives, with a few quirks, roles and stats switched about. The soul is eternal, but a name is worldly. As far as we know, Rand and the Heroes of the Horn are the only souls who consistently are identified as the same person each time.

For all we know, Nynaeve might have been Latra Posae Decume but in this Turning of the Wheel, she is less obvious about her opposition since Rand needed a support system.