I am aware that "Sunday" and "Monday" pretty much derive from sun-day and moon-day respectively. Why do we use these quite English sounding day names instead of naming them something like "Apolloday" and "Vestaday", honoring ancient Gods like the names we use for the other days of the week?
None of the weekdays are named after mythological figures. They’re named after planets. Their names Saturday (Saturn), Sunday (the sun), and Monday (the moon) are vestiges of the ancient seven day astrological week developed in the first century CE, which was synced up with the seven day cycle of the Biblical Jewish week. The astrological week assigned time rulerships to different days: Saturn for Saturday, the sun for Sunday, the moon for Monday, Mars for Tuesday (mardi, in French, and martes in Spanish), Mercury for Wednesday (also mercredi and miércoles), Jupiter for Thursday (jeudi or jueves), Venus for Friday (vendredi or viernes).
The ancient astronomers and astrologers among us might notice that the astrological week doesn’t follow any standard planetary order used in antiquity, such as: Saturn, Jupiter, Mars, Mercury, Venus, Sun, Moon, which was used in the Hellenistic period; or Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon, sometimes with the inner planets switched around, the so-called Chaldean order generally used by the Romans. Both are based on perceived length of revolution, and thus distance from earth, which is why the result happens to also closely mirror the distance of the planets from the sun.
This lack of correspondence, though, between the days of the week and the planetary order is actually something of an illusion, because the Roman system of time rulerships was actually based on hour rulerships, not solely day rulerships. So if you were to take, as the Romans did, the planets of the Chaldean order (Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon) and assign them in order to the twenty four seasonal hours in a day, you would find that if Saturn was assigned to the first hour of Saturday, and proceeded through the seven planet cycle, the first hour of Sunday would belong to the sun, the first hour of Monday to the moon, and so on, and the pattern of hour rulerships would repeat every seven days based on the number of planets used. Individual hours within those days also had their own time rulers, so that every period of time had both an hour ruler and a day ruler.
So how did you actually use these time rulerships? In the ancient astral tradition, planets could have benefic or malefic qualities: Venus and Jupiter were malefic, Saturn and Mars malefic, and Mercury was common (i.e. if paired with a benefic planet it is benefic, if paired with a malefic it is malefic). So the eighth seasonal hour of daytime on a Friday, an hour ruled by Venus on the day of Venus, was especially favored, but the sixth seasonal daytime hour, ruled by Mars, was still noxia, “noxious”, because it was ruled by Mars, a malefic planet. We have found the fragment of an inscription from the late first century CE that preserves part of a table listing out the B(ona), C(ommunis), and N(oxia) hours for either a Friday morning or a Monday night (we’re not sure which, because we have no way of knowing whether we have the beginning of the day or not, as that part isn’t preserved), putting this system on public display. The only published photo of it anywhere is in Heilen, cited below, which includes a drawing of it with a partial reconstruction. We also know from Juvenal (Juv. Sat. 4.572-583), who describes women who use them, that books existed that included these tables for those who wanted to be able to carry them around with them.
Our modern Saturday, Sunday, Monday partially preserves this Roman astrological tradition and the planetary order it used to assign units of time astral significance. The association of days with deities is based on the theophoric naming of planets rather than random mythological assignation. The modern names and the cultural associations of the weekly cycle have changed over time, so the French dimanche and the Spanish domingo no longer have any relationship to the sun and the English names for Tuesday through Friday have shifted, but the core ordering of the astral week remains.
Bultrighini, Ilaria and Sacha Stern. “The Seven-Day Week in the Roman Empire: Origins, Standardization, and Diffusion.” In Calendars in the Making: the Origins of Calendars from the Roman Empire to the Later Middle Ages. Edited by Sacha Stern. Brill, 2021. 10-79.
Heilen, Stephan. “Short Time in Greco-Roman Astrology.” In Down to the Hour: Short Time in the Ancient Mediterranean and Near East. Brill, 2019. 239-270.