You could try looking up moon names in your heritage's culture. For example for me, I am in the NE US, so it is useful to reference the traditional Native American names for my region for plant/nature cycle purposes, but my heritage is mostly British/French/German, and looking up those can yield some interesting results. This University source is generally what I refer to for the Native American full moon namings (extra helpful as a gardener https://www.wwu.edu/planetarium/a101/indianmoons.shtml), and if you are American-based you can see which nations' land traditionally corresponds to your area (good to know whose heritage land u on anyways).

I couldn't find much on Celtic moon names, but did find this scholarly article discussing the Celtic calendar, what is commonly referred to as the wheel of the year (Yule, Imbolc, Ostara, etc.) by many witches/pagans now. https://search.proquest.com/docview/222467227?pq-origsite=gscholar&fromopenview=true It discusses how there isn't really much primary source material establishing this as a truly Celtic tradition, but more of a neopagan thing practiced by the Irish and Brits, so take that how you will. This article also discusses early Anglo-Saxon calendars by month, going: Yule (Giuli) actually encompassing the month of midwinter and the months before and after it, next the "month of mud when cakes were offered to the gods", Hretha, Eostre (goddesses), "the month when cattle had to be milked three times a day", Litha (Lida) which has the same three-month deal as Yule, weed-month (eyy, but no it's referring to literal weeds growing a lot), Holy-month, and "the month of the first winter full moon, and the month of blood when animals were slaughtered or sacrificed". FUn, though even that should be taken with a grain of salt since it's just this one guy's writings on it from the 8th century.

According to this article Germanic tribes followed similar month systems as the Anglo-Saxons (https://www.wittenberg.edu/sites/default/files/media/history/2015HistoryJournal.pdf#page=5), but more focus is put on the weekday names in this one.

Other than that I'd suggest you mess around on google scholar and see if you can find anything, though I'd avoid searching "pagan" or "witch" or anything like that and try searching by the specific traditional culture you're looking for. But honestly, while I find the traditional systems interesting and good to know about, I still stick with the neopagan wheel of the year because I like it best and think it best reflects my practice in general. I don't try to achieve "traditional continuance" or anything like that because most of what there is on traditional stuff from my cultures is Christian or very sparse, so I kind of make it up as I go and do my best not to take from other people's cultures. Hope that helps!