The title "white king" doesn't necessarily mean that the king had white skin. The egyptians recognized that this universe was created (and continues to be created) by the interaction of opposites. (man+woman+child for example) (the two lands, white and red is another, from them comes egypt, the nation)This natural law was at the center of everything they did. R.A. Schwaller de Lubicz shows in The Temples of Karnak how the names of the pharaohs reflected this understanding and how there were occillations between the Sethian pharaohs and Ra-mese pharaohs. The carvings that represent one sides work are carved into the stone while the work of the others are bas-relief. One enters into the stone and one emerges from it. I think that there was this back and forth and what Akhenaten represented was an attempt at synthesis of the two into one. Aten was represented by the sun, which in itself is a manifestation of that balance between explosion(out), and gravitational implosion(in)-the result being a sphere, balance. So white can represent more than just skin color. It can represent an aspect of a natural duality, I dont know if that is true for the king that you mentioned, but this concept can be found all over in AE.