Have you asked the nymphs what they use to call themselves?
Ok, not entirely kidding. You could do worldbuilding... dig into the culture and perhaps the language of the nymphs to get ideas. ("Daughters of the Sea," in "sea nymphian"?) And maybe they use "the people" in the common nymph language for "nymph"... which may be a "Bahasa Indonesia"="Indonesian language" type of thing...
Perhaps there are religious concepts they use to name themselves? Historical? Mythological? (And I mean "nymph" mythology here... is it the same as the Greeks? Why? Why not?) Etc.
Looking at minorities or people far away from the culture I'm in, it seems most of the time the names used by my culture are not the names that people use for themselves.
I think one of the most glaring examples is "Indians," where we've gotten so far as to call them "Native Americans" while they, themselves use many different names. And you could look at the etymology of the names to get an understanding of their meaning. E.g. the "Sioux" (which incidentally is a French evolution of "Su" I just learned!)
To lend credibility to your story, having a "nymph" go, "yeah yeah, you call us nymphs, I know... I don't..." would be a realistic touch.