Hydaelyn's Star

[Myranda]

The star that Earth orbits around is technically called "Sol" but no one calls it that (except in Spanish). Maybe the star at the center of Hydaelyn's system is named Azeyma but everyone just refers to it as "the sun".

As they commonly refer to Menphina as just "the moon", I'm sure they would just call it "the sun" in all casual conversation as you suggest. In fact, I'm not sure I've ever even seen either referred to by name in the game, it's all just been extrapolation from Dalamud being the hound of Menphina and the association of Menphina/Azeyma as moon/sun gods.

I will note though that, contrary to what sci-fi stories would have you believe, our own RL star's name is NOT actually Sol, it's officially just "The Sun" (capitalized). Nor is our moon Luna, its just "The Moon". Like your note about Spanish, these are just the Latin translations for the two, not official names for them.