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Having no identity can be useful in certain situations. So much so that the game GURPS has an Advantage called Zeroed, which means that you don't exist in any official records or databases. It means authorities can't track you down and bad guys can't use publicly available information about you to do the same, or indeed to find out anything at all about you. This is a deliberate thing - steps have somehow been taken to ensure that, officially, you don't exist. It gives you perfect anonymity and cover for covert operations.
Of course it can make it difficult to do things like buy a house or take out a loan.
Commentary by memnarch (who has not seen the movie)
Bwahahahaha! This is probably just to explain why Kylo doesn't immediately zero in on Han and Chewie in the movie with some other Force Power, but who cares; this is great! It's like the Summon Bigger Fish result again! And interestingly, Chewie isn't described as being sensed here. A fortunate side-effect of him technically being a sidekick?
Anyway. Han is probably dead this time. I can't think of any other potential places for names to go after "Mr. Nameless" and this situation also looks pretty bad. Chewbacca dead? I hope not, but I can't see how Han getting caught and killed wouldn't lead to Chewie also being caught and killed. Maybe he blows up all of the explosives as a distraction, but that would probably get Han along with most everything else. I also don't know what happens to sidekick characters in this game system; familiars seem to die with their master, but that could just be a result of the psychic link. If Chewie doesn't kick the bucket though, this is going to be an odd inversion of that Star Wars comic where Chewbacca dies because of a moon somehow falling on him.
Transcript
GM: Kylo Ren receives a report of a disturbance in the main weapon systems hexagon.
Kylo Ren: I stalk over there immediately with a squad of troopers.
GM: You enter the catwalk room.
Kylo Ren: Force Sense. Oh, 5.
GM: You sense a presence, but it’s vague and undefined... like someone with no identity.
Kylo Ren: Find them!
GM: Troopers fan out, covering all the levels.
(No Name): I stay hidden and silent.
GM: That implies that you were hiding silently already.
(No Name): Good to see you’re up to speed.
GM: Next you’ll be telling me your characters have all been holding their breath ever since the Trade Federation waiting room.
Chewbacca: That would explain their distinctive cognitive peculiarities.