Names & Titles:

Galadriel
The Sindarin name Galadriel means "maiden crowned with a radiant garland," referring to Galadriel's beautiful hair. The word galad means "radiant" in Sindarin from gal or kal meaning "shine." The word riel means "garlanded maiden" from the root rig meaning "twine, wreathe." According to one tradition, the name Galadriel was given to her by Celeborn.
The Silmarillion: "Appendix - Elements in Quenya and Sindarin Names," entry for kal
Letters #345 & #348
Unfinished Tales: "The History of Galadriel and Celeborn," p. 231

Galadhriel
Some Elves outside of Lothlorien, to whom Galadriel was merely a legend, referred to her as Galadhriel because they mistakenly interpreted her name to include the element galadh, meaning "tree."
Unfinished Tales: "The History of Galadriel and Celeborn - Appendix E: The Names of Celeborn and Galadriel," p. 267


Altáriel, Alatáriel:
Altariel is the Quenya version of Galadriel. The word alata is the Quenya equivalent of galad, meaning "radiance." The Telerin version of her name is spelled Alatariel.
The Silmarillion: "Appendix - Elements in Quenya and Sindarin Names," entry for kal


Artanis
Artanis was Galadriel's father-name - the name given to her by her father at birth. It means "noble woman" in Quenya. The element ar means "noble, royal" and the element ta also means "high, noble, lofty." The element nis means "woman."
Unfinished Tales: "The History of Galadriel and Celeborn," 231
The History of Middle-earth, vol. V, The Lost Road and Other Writings: "The Etymologies," entries for NDIS and TA/TA3


Nerwen
Nerwen was Galadriel's mother-name - the name given by her mother. It means "man-maiden," in reference to Galadriel's unusual height and strength. The word ner means "man" and wen means "maiden."
Unfinished Tales: "The History of Galadriel and Celeborn," 229
The History of Middle-earth, vol. V, The Lost Road and Other Writings: "The Etymologies," entries for DER and WEN


Lady of the Noldor
Galadriel was the noblest lady of the Elves called the Noldor.


Lady of Lórien, Lady of the Golden Wood, Lady of the Wood, Queen Galadriel
Galadriel was called by these titles because she ruled the Golden Wood of Lothlorien.


Lady of the Galadhrim
The people of Lothlorien were called the Galadhrim, or the "people of the trees."


White Lady
Galadriel was referred to as the White Lady. She had fair skin and often wore white robes, and she seemed to shine with a white light. The name is also a contrast with the Dark Lord, with whom she was in opposition.


Sorceress of the Golden Wood
Grima Wormtongue called Galadriel the Sorceress of the Golden Wood, falsely insinuating that she wove webs of deceit.
The Two Towers: "The King of the Golden Hall," p. 118


Mistress of Magic
Galadriel was called the Mistress of Magic by Faramir.
The Two Towers: "The Window on the West," p. 275