(Reworded my post with some new ideas)
The names for the organisation could be Farbauti and Laufey (or derivatives), which as you probably know is Loki's parents which is fitting because the man who created the cyborgs has his name based off of Loki.
Instead of switching sides we could also have him leaving her and being confused over who he is, his purpose and stuff like that which brings him to realize that he loves her and if Ragnarok goes ahead she will be killed and so will the city/state? I just think it would be unlikely for him to randomly change sides, you know a bit of an impulsive/rash decision from his point :/
Yeah a good ending would be good, where they actually beat them (and lives with the girl/cyborg of his dreams? :L)
I really like this idea of having the names based off of the gods and such from the Norse Mythos, works very well I feel also if we were to chose a floating city we could call it Asgard as it's a floating city and that's like their version of heaven? Also would there be any place where we could maybe fit the Valkyries as characters into it? Maybe like hunters from on the corporations tasked with finding Jett maybe?
Also what do you mean by exaggerating with elements? As in the names based off of the myths?