I don’t think their names are all Greek, but rather summon or older FF related.
Artemis was a pull from FF8, not necessarily Greek.
Like, I think Elidabus is actually named “Sabik”.
Rabbit hole time:
1) Elibabus of FF12 is associated with the constellation Ophiuchus, which in the real world contains the star, Sabik.
2) The Heart of Sabik is supposively a pre-Allagan device that they could only use as a power source.
3) The heart consumed Aether (primals) and fed Ultima Weapon.
Tin foil hat time…
4) I believe the heart is of Ancient make in an attempt to replace Elidabus as the heart of Zodiark, and possibly make “feeding Zodiark” easier.. as in feed him primals and not necessarily the lives of lesser beings. I don’t think this is Ascian-make, but maybe Venat or Azem.
5) Alternatively, this has nothing to do with Elidabus and was an attempt channel excess aether from “the sound” to stop the nightmare summons.
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I expect the Ascians, if named, to have big famous and kinda “left field” names. Like Byrnhildr or Balthazar. We have to remember they are starting to run out of main-title references (like the only real summons we haven’t seen are what.. Tritoch and Maduin? Asura?)
Given the nature of The Sound and the flying city art, I would not be surprised to see Chrono Trigger references like Mammon or Melchoir. Or pulls from other SE properties.