Use of real gods in a fantasy setting
This is something I've been thinking about and can't come to a decision on, so I wanted to ask here
The setting is 'historical' low fantasy with anthropomorphic animals, the location the story takes place is very heavily based on the British isles in terms of culture and linguistics. Generally the people there don't have a god, simply spirits or ancestors
Our main character is from a far off land, The many Isles of the Emerald Sea (The Emerald Isles), which I am basing on ancient Greece. She worships the Hellenic pantheon and references a number of myths as a way of sharing her culture and making the people comfortable with her being there.
I have been using the Greek god names so far (our MC is a Huntress of Artemis) but I was wondering if I should change them and if keeping the real names would detract from the fantasy aspect.