Disclaimer: Tolkien's.
AN: This is Galadriel's history through the long ages of the world, told in the naming and the names themselves.
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Artanis she had been in the West. Artanis was the Kinslaying, the Helcaraxë, the years of war and blood and death. Artanis was not someone she wished to remember, and Nerwen she had only been to the mother she had left on the shores of Valinor. She was Galadriel now, Alatáriel, as he had named her. A new name, a new life, a new hope.
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She is born in the light of the Two Trees. Her father named her Artania, because that was what she was. She grew up longing to follow her three older brothers about here and there, wishing she was born one of them. Instead, she was expected to sew intricate bead-work and learn to stitch with gold and silver threads. Her life was gardens and verandas and women's rooms. Artania respected that her father was a king amongst the elves and that that made her, if not a princess, at least a lady-to-be. But where others, including her mother, appreciated a life of little care and little worry, as a young elven maid she desired still more.
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Artania was newly come to fifty summers, consider to be not yet an adult and no longer a child when her mother named her Nerwen. She liked it more, because it was what she was starting to become and longed to be. Noble she had been born, but she wanted more than that. Her mother saw in her power veiled behind innocent eyes. She could do anything her brothers could do, if only she were allowed, and her mother knew she would do even more.
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Doriath is not a place to escape the past. Thingol will dredge up old cares at the least opportunity and there are many who know the truth who come and go through the forest. Rumours have spread faster than wildfire on the mountainside. Nerwen finds safety only in Melian's presence, content to spend whatever time the queen is willing to give learning all that she might consent to teach. Nerwen still desires power, no matter what its seeking has already cost her family. Melian is not so easy to fool as her husband, but she gives knowledge for those who seek it and Nerwen is certainly willing to seek.
She meets him in the first years after she comes to dwell in Thingol's fading realm. He is fair and wise already in his years, and less rigid than she. He has known war already and hardship, despite his kinship with the forest's ruler, but it has not effected him in the way it has her. She tells him her name the first time they meet and he has the gall to laugh at it, asking if she named herself such. He looks only thoughtful when she tells him it was her mother who chose Nerwen and he wonders aloud if Eärwen might have more foresight than she knows.
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When he asks for her hand, he says he will give her a new name if she accepts. There are many reasons to say no, for she has ever been her own woman, but she accepts despite this. Celeborn has power, in his kinship and in himself, and together she foresees they could do much. But she is growing tired already in the woods of Melian's girdle and she longs for other lands. He offers to show them to her. And so she takes her new name, Alatáriel, and begins again. She can leave the past behind now, to live from this moment forward. She can make a new mark on this already scared land, find new realms to rule and more power to acquire, and she can do it all with a great silver-haired lord at her side.
For although Celeborn has never seen the Two Trees, he knows well of their story, and it is not without some foresight that he names her anew. She has brought the light of Valinor with her across the ice, and in her hair is all that remains of their radiance in Middle-earth.
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Sindarin does not become the common language of converse amongst the Eldar in Middle-earth until the Second Age. Partly it is an easier form for all to acquire, particularly the Dark Elves of the east, but the forest elves of the midlands find it preferable as well, over the Quenya that is quickly becoming a scholars' tongue, and a language only of court.
It is the forest elves of Eriador at the end of the First Age that name her Galadriel, because they would name her in their own tongue. She finds she prefers it, especially in their speech, and allows anyone who wishes to call her thus. Alatáriel she reserves for Celeborn, who will not call her anything else, for its language is his birth tongue and still and always will it be his name for her. And she is glad for that, for it is the mark of her new life.
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In later years, when she rules Lórien by Celeborn's side, some will call her Galadhriel. The first time she laughs because it cannot be expected that all elves will understand the linguistics of it, and the mistake is understandable enough. But it is not her name, and she corrects any who she hears use it. She is not a tree maiden, no matter that she lives in the mallorns of the forest. And yet, the name is a badge of honour nonetheless, for it represents the people she now rules, and perhaps it is no less a noble title than Nerwen was.