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You can manage without one, but I'd recommend against it, unless you have a compelling reason. A protagonist without a name is often awkward to write, and certainly awkward to think or speak about...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/21490 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
You can manage without one, but I'd recommend against it, unless you have a compelling reason. A protagonist without a name is often awkward to write, and certainly awkward to think or speak about. A character's name is a pretty basic, fundamental aspect of their identity; there's something _weird_ and forced about deliberately avoiding revealing his name. There's also the simple fact that the reader _expects_ to get a name; if the reader doesn't get one, he's going to think that's a little odd. These are all things you can overcome, certainly in a short story that can stand a little weirdness. That might be worth doing - **if** you have a good reason for it. That's what's happening in the examples some of the others have given: - In _Rebecca_, the protagonist has no name; she's only known as "the second Mrs. De Winter." That emphasizes how her own name _has become unimportant_; her identity is being subsumed in her marriage, how she's constantly being compared and contrasted to Rebecca. - In _Fight Club_, there's good reason to conceal the protagonist's name - there's a major twist involving it at the climax. It also represents how the character feels hollow, fading away, a nobody. Those are good reasons to leave a character nameless. If you have a good reason, a short story can certainly bear that weight. But if you just don't have a name for them, or if having a nameless character is just an arbitrary decision, then you're probably better off choosing some name and avoiding the issue.