- "...and Anar the Fire-golden, fruit of Laurelin, they named the Sun. But the Noldor named [it] Vasa, the Heart of Fire, that awakens and consumes; for the Sun was set as a sign for the awakening of Men and the waning of the Elves..."
A poetic name for the Sun was The Daystar, and Gollum referred to it as The Yellow Face.
The Sun was seen by the Elves as made in memory of Men, and they valued the Moon higher. Morgoth's creatures, the Orcs, feared the Sun, and with the exception of the Uruk-hai, they did not travel while it was in the sky.
Other versions of the legendarium
In the early versions of The Silmarillion as described in The Book of Lost Tales Part 1, a part of the History of Middle-earth series, the Sun was described in great detail as an immense island of fire. It was also said there that the youth Tilion, who guided the Moon, was said to secretly be in love with Arien, and that because he steered the Moon too close to the Sun the Moon was burned.
In writings not included in the Silmarillion tradition, Morgoth at one point was infatuated with Arien, and wanted to claim her as his wife: he is at one point even described as ravishing her, so she abandoned her body and 'died': the Sun after this for a while left its course, burning a large part of Arda the world (apparently creating the deserts of Far Harad). It is not clear if this would have been included in the Silmarillion had Tolkien lived to publish it himself.
In the Round World version of the legendarium, the Sun and the Moon were not the fruit of the Two Trees, but actually preceded the creation of the Trees. Instead, the Trees preserved the light of the Sun before it was tainted by Melkor when he ravished Arien.