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Invoked: A character refuses to tell anyone his name, not in a serious effort to protect his identity, but simply because being The Man With No Name is so very enigmatic and badass.
Defied: The main character wears a shirt with their name on it.
Discussed: "What's the big idea not telling anybody your name? It's not like people don't recognise you anyway"
Conversed: "It would be cool to be one of those movie characters who don't tell anyone their name. But I bet it's hard to get a bank account".
Deconstructed: The character has to live completely off the grid to maintain their anonymity, and the authorities are extremely suspicious of their lack of any identification. They're generally mistrusted by other people as well, and can't form any close relationships unless it's with a single loyal Secret Keeper.
Reconstructed: Their anonymous existence allows them to stay off the radar of a totalitarian government, and the few people they trust enough to reveal their name to know they're part of a highly exclusive circle of friends.