Names should reflect their place in the story.
I use period human names for humans in my stories. Even mixed cultures can have mixed names, an elf by the name of Bob, would be strange, but it could happen. We name babies after special people, and sometimes those people are from a different culture.
Modern names used in old worlds would be wrong, and would seem lazy.
Just as names for other races using all human names would be wrong. Look at the various ethnic names of the world. Hispanic, African, the various oriental names all have unique names, so imo all different races and cultures would have different names.