I think Rand "The Dragon Reborn" al'Thor will die. The name will die and the popular belief will be he has in fact perished. Rand will no longer be able to command the armies, countries, etc. from the general populace after TG because the Dragon (the person so many people know about) will have died but Rand himself, Rand the person will live on but not in name. It will be recorded in history that Rand perished during TG.

This makes the most sense with the image of his women crying over his body and the vision that Alivia will help Rand die and all of the other visions which I can't think of off hand.