I always assumed it was related to the word "azimuth" - the etymology of which originates in the Arabic word as-sumūt, meaning "the directions" or "the paths". Azimuth is often used in navigation to express direction, and it fits nicely into the idea of the seat of Azem being a traveler. Not to mention that azimuth is also used to describe the sun's position in the sky.
Or maybe they started with Azeyma, and then just fit Azim and Azem both together with it?
