It seems to me that the powers she displays in ToM were akin to what Rand did in the end with his pipe, as well as how he made food taste good again. She seemed to have managed to add more coals to the fire, and make delicious food. Plus, the inspiration for her comes from deep in RJ's notes on Rand. All this suggests there is a connection to Rand.
Another thing to note is that Nakomi's name is an obvious derivative of Nokomis, an Iroquois name meaning "Daughter of the Moon" as well as "Grandmother". These names can fit Lanfear very well, but even though I can imagine a situation where she wants the Aiel to survive, I can't see her helping Aviendha of all people, nor can she possibly have said anything to Rand when he came out of SG (she was dead by then).
The only other character that can be called Daughter of the Moon, and Grand Mother, is Egwene. I really resist this idea, because for Nakomi to be Egwene, we'd need to have time travel involved.
But consider these quotes:
Its been constantly remarked that Egwene could easily be Aiel. She even considers that she has an Aiel heart... could she just be Aiel at heart?
And then there's the manner of her death. One way or another, her weave plays with time. Its supposed to freeze someone in time, but what if it does more? After all, there are ripple effects to balefire's burning of threads back in time. What if there are ripple effects to the Flame too? What if, instead of unspooling the Pattern, using the Flame does the opposite, and creates events in the past that allow the Pattern to be stabilized in the future?
This is admittedly so far out as to be ridiculous. But perhaps by this or some other mechanism, Egwene was actually there for Aviendha and the Aiel, and is responsible for the remnant of the remnant (the heart of the Aiel?) surviving?
And her role with Rand in the end also would make sense. We had a lot of foreshadowing of Egwene "killing" Rand. Instead, she nudges him along the path that will "help him die" but not kill him.
So, my theory is this: Nakomi is an ancient name, referring to a soul that's a counterpart to the Dragon's. She complements his purpose (as did Egwene), and also has strong ties to the Aiel. Perhaps her last birth was as an Aiel Wise One, and this is the form she choses to take even after her death in this life. After the death of Egwene's body, perhaps because of the manner of her death, Nakomi was able to do several things. Firstly, as Egwene, she conversed with Rand about death. Then she saw to the Aiel. Then she returned one last time to nudge Rand towards his "death".
And a little bit more to hint at a connection:
Egwene does seem to "see to nature" quite a bit in aMoL.
Anyway, this is admittedly a whacky theory. Feel free not to add Egwene to the voting list. But... thoughts?
I like it. Very interesting, especially the part about it being a counterpart to balefire. I bet you many of the answers we seek will be revealed when we see these issues in the light of Jordan's fundemental concept of this series, the idea of balance.
One or the other alone doens't work well, but together things are as they should be.