Azeroth has a single sun. Draenor, or at least the shattered remains of it, likely orbits the same sun, due to the relative closeness of the two evidenced by Azeroth being seen from the Black Temple raid. However, Azeroth may be seen through a portal-like "window", as some other worlds were speculated to be in Unbroken.
As subject of worship
The blood elves and high elves symbolically revere the sun as opposed to the night elves who worship Elune, the goddess of the moon. Blood elves and high elves use the battle cry Anar'alah belore! ("By the light of the sun!") or often greet each other with the phrase Anu belore dela'na ("The sun guides us") in Thalassian. Most of Quel'thalas' denizens do not speak of it as a star or as an astronomical phenomena.
The tauren refer to the sun as An'she, the right eye of the Earthmother, in the in-game book Sorrow of the Earthmother. In the wake of the Cataclysm, tauren have learnt to wield the power of the sun, giving birth to the Sunwalkers.