Cordae

Cores are strong sources of unstable reality within the Abyss. These are what draw souls in from other worlds to the place between worlds (and maybe Atal). It's not completely wrong to say that Cores are made of souls but in some cases, some souls manage to maintain themselves. Since these souls are tied directly to their respective Cores, they cannot leave their respective Domain. They also can achieve incredible feats of magic. However, if they aren't careful with their magic, they may go insane. Plus if they leave, they will either disappear or be complete absorbed by the Core they serve.

Thus, their goals would most likely be to stabilize Atal so they aren't needed or somehow cut them off from the Core.

Biology Based
The name Septer was inspired to the two words scepter and septum. These are the ones whose souls are directly connected to the Cores.

To be honest I'm thinking of changing the names into "Cavi" from the word cavity or the "Percardi" from the word pericardium.

I'm up to suggestions. "Septer" makes sense since these beings/people essentially control and are manifestations of magic. It gives them the whole "royals and their rule" kinda vibe. At the same time though it doesn't make complete sense given what become of them...

Plus names like Cavi and the Percardi kinda sound more fancy like. I might just combine the two into "Percavi."

Other Based
Amalga from the word amalgamation

Einmes from the German word "ein" and the Spanish word "mezcla"

Mezclar is Spanish for "to mix"

Beon is Old English for "being" (though the actual word has some sort of accent over the o."

Cor from Core

Guardian for obvious reasons

Corda is latin for cord (I think I might just go with this one)

Nah I should call them Corn.