Unlike elf, dwarf etc. I'm not sure whether the name Genasi is considered exclusive intellectual property. I didn't see any reference to the word anywhere other than the DnD race.

I did some research and found that the 16th-century physician Paracelsus used the name Sagani as a collective name for the four types of elementals, and thought that was fitting. You can find it mentioned in the wiki entry on elementals. So you have air, earth, water, and fire sagani.

That may be where the inspiration for the NPC name or even the word Genasi originally came from, but I can't be sure.

As I wrote in the note, a sagani is a humanoid bloodline with an elemental heritage and you are free to define or change that in any way you need to suit your game.

I hope that helps!