Well, how did they get to Earth? Nicknames can be taken from anything. My immediate thought was "Skimmers"... in my head your creatures "skim" reality to end up at Earth (though I'm sure that's not how it works in your story). I also thought of "the Others", but that's the title of a ghost movie. For those of us who don't play D&D, "Outsiders" is vague enough not to be associated with it, although for your purpose that wouldn't work as well for non humanlike creatures. Slips? (did they slip through reality instead of skim it? lol) Shifters? Drifters?
What sorts of creatures are these? You can also get nicknames from appearances, or sounds. Howlers, Screechers, Hunters, Prowlers (no, not a car)...
What was the first of these creatures to "discover" Earth? You could name the whole group after the first unlucky bastard to get eaten/killed/whatever by one of these things, or name them after a scientist who has tried to research/classify them. "I think we have a Darwin in the area..."
I dunno. That's a tough one.