Every once in a while, someone in the community brings up the 'Hellenic days of the week', a seven day calendar with Gods attached to certain days and special names to call these days. In general, the following is the standard:
  • Monday: ἡμέρα Σελήνης (hêméra Selếnês) – "Day of Selene"
  • Tuesday: ἡμέρα Ἄρεως (hêméra Áreôs) – "Day of Ares"
  • Wednesday: ἡμέρα Ἑρμοῦ (hêméra Hermoú) – "Day of Hermes"
  • Thursday: ἡμέρα Διός (hêméra Diós) – "Day of Zeus"
  • Friday: ἡμέρα Ἀφροδίτης (hêméra Aphrodítês) – "Day of Aphrodite"
  • Saturday: ἡμέρα Κρόνου (hêméra Krónou) – "Day of Kronos"
  • Sunday: ἡμέρα Ἡλίου (hêméra Hêlíou) – "Day of Helios"
This website seems to be the source, which, in turn, seems to be based off of the work of Roger S. Bagnall. This research can be found here, and show that the idea has been taken out of context entirely. To quote the paragraphs surrounding the calendar:

"The seven-day week is well attested in Greco-Roman sources, although it was not the only cycle operative in antiquity. The ancient Greeks and Egyptians had a ten-day week, and the Romans observed, in addition to the seven-day. The use of numerals to identify days of the week is seen especially in late inscriptions. The way in which the planets were ordered depended on their perceived order of astrological dominance and not on their presumed distance from earth. This arrangement was informed by the belief that a planet exerted influence over each hour, and the planet that governed the first hour of a 24-hour cycle ruled that entire day. Saturn, the planet farthest from earth, ruled the first hour, and so Saturday began the week; the hour was governed by the sun, so Sunday marked the second day, and so on. Dio Cassius attributed the introduction of the planetary week to the Egyptians, although he acknowledged that the custom was observed elsewhere, too.

When exactly the practice was adopted in the Greco-Roman world is uncertain. We find the first clear evidence in 1st-century CE graffiti from Pompei in which the planets are listed in the order of the planetary week. Earlier references to days, such as several well-known examples found in Latin poetry from the 1st century BCE, attest some preoccupation with a belief in the astrological significance of planets for human affairs, but they do not prove observance of a seven-day week. Similarly, in a small number of Hellenistic and Augustan-period texts we encounter references to the Jewish Sabbath, but these again do not prove that the seven-day week was widely recognized throughout the Greco-Roman world, as it was in Jewish society where days other than Friday and Saturday were numbered. All we can say therefore is that by the 1st c. CE the custom had been established in at least parts of the Greco-Roman world. More abundant evidence for it is to be found in later periods."

For most of their time period, the ancient Hellenes had a 10-day week, fitting three weeks into a lunar month. They were called 'decads':
  • First Decad - Waxing Moon - Mên Histámenos
  • Second Decad - Middle Moon - Mên Mesôn
  • Third Decad - Waning Moon - Mên Phthínôn
In ancient Hellas, days in the first decad were labelled 'the [number] of the waxing moon', or 'the waxing [number]'. Days in the second decad are labelled 'middle [number]', either from 'middle first' to 'middle ninth', and then on to 'early tenth', or from 'middle one and tenth', to 'middle nine and tenth', then on to 'middle twentieth' (or 'early tenth'). The proper labelling of the last decad is 'the [number] of the waning moon', or 'the waning [number]', but they could be counted back from the coming new moon. 'The waning third', for example, is often considered the twenty-third day of the month, but could be interpreted as the twenty-eighth.

While the monthly lunar calendar (the 'Mên kata Theion', 'sacred month') included a lot of recurring sacrifices to the Gods, and while the days did have names sometimes, they did not always relate to a specific deity, and most certainly not in a weekly rotation.

It's fine to use this Roman calendar to honour the Gods; everything is fine as long as you feel you are honouring the Gods well. Is it Hellenismos, though? Not really, not Traditionally so, anyway. The Mên kata Theion is far more accurate for that. Advertising this seven day calendar as 'the calendar of Hellenismos' is therefor false; it was a Roman invention, based off of the ancient Egyptians and most likely even older cultures. It existed in the time of the ancient Hellenes, but it was not the prevailing sacred calendar.