"Ilyena Sunhair", Rand holding the Sun Throne for Elayne, etc. Even the names are similar, differing by one letter with a little jumbling. Both are described similarly, and both are very prominent in Rand's affections.

If Ilyena is indeed LTT's "soul mate," it might be the she's split between Rand's three women at the moment, but that could be a stretch. They could always just be three knew souls. My guess is that RJ left this for us to speculate, but really had no real answer.