Caller would fit in world. We already have the Sarkoris god callers. It is a different relationship, but useful one for concepts.
Sarkoris God Callers are summoners.
Summoner would be confusing just because of the class by that name.
I think they intentionally left the terms of the contract vague because there are all sorts of potential contracts. My preference would be one that is mutually beneficial, but I don’t play many characters that are neutral.