It depends on the coven/group. Celtic pagans call themselves that or sometimes Celtic Wiccans or just pagans.
It's the pagan beliefs that are rooted in Irish and Welsh history specifically. Then you have different pagan beliefs that are rooted in Norse theology or Greek mythology.
My mom raised me as Wiccan. There's about as many denominations as there are in the Christian religion.
Edit: Sometimes they'll even call themselves Druids or follow Druidism.