In Homer, Helios is sometimes called Hyperion, an older Titan-aspect of the sun god, the one who walks “above” the sky. The two names get used interchangeably for the god of the cattle on Thrinacia. The retelling drops the older title entirely. Helios is just Helios, the Sun, and that is all the page needs. Hyperion belongs to a deeper layer of Greek myth, the generation before the Olympians, and pulling him in would have meant pausing the story to explain Titans. Easier to let the Sun be the Sun.
Hyperion
The Titan name behind Helios. Not used in the retelling — the Sun goes by his working name.