I don't think the ascians that give the crystals to Tristan have names, it must be Random Ascian #576 or something like that, as for Elidibus I think it's more because they needed a name for the opposite to Zodiark as he and Ultima didn't have one so they picked Elidibus name and Ultima's ascian just called herself Ultima, so I don't think we can really be sure that it means that they can summon them, although it would be really cool !