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All the way back to A Wizard of Earthsea, the Names-Have-Power trope usually handles this by giving people nicknames for "public" use. Their real names are closely-guarded secrets. You can definit...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/21440 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
All the way back to _A Wizard of Earthsea_, the [Names-Have-Power trope](http://tvtropes.org/pmwiki/pmwiki.php/Main/IKnowYourTrueName) usually handles this by giving people nicknames for "public" use. Their _real_ names are closely-guarded secrets. You can definitely give your protagonist a nickname; that's what people would do in the situation, because you have to call her _something_, and that also solves your problem. If you want to emphasize her namelessness, you can put focus on how these monikers are nicknames, not her real name. One idea would be for different people to use different names; none of the nicknames "catch on" and become a widely-accepted name for her. You could even have her give a nickname to herself, if you need a name she gives herself from her own POV.