Hey look, my game's being used as a reference! Yay! Funnily enough I didn't actually come up with the name for the Remnants, but I like Sentinels "The Omega" if you're going for cold, unemotional robots. If you want them to basically be humans in that they each have personalities and consciousnesses, you might want to add a faction-y sounding thing onto that, like the Omega Syndicate or the Omega Union.
As for the game itself, it really depends what kind of theme you're going for. Heroic adventure game, gritty "war is hell" type thing or whatever, because some work for some themes and some don't. I'll throw out "Blood and Rust" because it's the first thing that came into my head.