What's wrong with "summon"? FFVII used the term, after all (along with changing up the usual spell names).

I liked Eidolon, until Fang pronounced it wrong, and used the incorrect term for the plural (it's "Eidola", Fang. Not "Eidolons").

I actually like them all. Pity we don't have a game which has all of them. Espers as another race of magical entities. Eidolons as guardian spirits granted by higher powers. Aeons as human crafted war beasts. Guardian Forces as Persona-like manifestations of thoughts and mental energies (as Griever indicates). It would be awesome.