I mean, yeah, many celestial bodies take their names from Latin. Like how the proper name of the sun is Sol, which matches solar, the lunar object would be called Luna. Selene feels like a retronym to match other Greek deities, and would be like renaming Earth to Gaia
either of those options is a fair pick given their oldness
Luna would definitely rank over Selene in the Western astronomical tradition. As you say, its name is just The Moon, which is what Luna means in many current day Latin derived languages