Everyone calls her Ana in FGO because she calls herself that trying not to be outed as Medusa during Babylon (Despite the MC already knowing anyway because it's kinda obvious if you know Rider Medusa and then see her) Ana is short for "Medousiana" which is pretty much the snakes Medusa has in her hair in lore.
Combine that with people not wanting to just call her Medusa Lily for convenience and there you go.
Do you want to sit too, Ana?There sure are a lot of stuff inside Osakabe-hime's room!A lot of books I haven't seen before!Doujinshi etc.Came to see the kotatsu.Ahaha...Oh? What's this?Aah, that's the cushion that can make people useless...A cushion that can make people useless...
How interesting!
