

All information comes directly from the writings of J.R.R. Tolkien. There are footnotes at the bottom of each section and a complete list of those writings used can be found here.
Artanis (Quenya)
The name given to Galadriel by her father, Finarfin. It is Quenya for 'noble woman'.
Nerwen (Quenya)
Among the Eldar of Valinor it was the tradition for the father to name the child at birth
(resembling the father's name somewhat), and then when they had grown a bit older the mother
would choose another name, "for the mothers of the Eldar had insight into the characters and
abilities on their children, and many also had the gift of prophetic foresight"1.
When Eärwen gave her a name, she chose Nerwen, which is translated man-maiden.
Alatáriel/Galadriel (Quenya/Sindarin)
In the Unfinished Tales we are told that Alatáriel was the name given to Galadriel by her lover (Celeborn). She chose to take the Sindarin form of this name (Galadriel) for use in
Middle-earth. Christopher Tolkien refers to this as her epessë, an 'after-name', which was a sort of nickname that was used throughout the histories and other such works (thus what the elf was best known as).
Galadriel has also been called the Lady of the Nolder, Lady of the Golden Wood, and the White Lady.
1 J.R.R. Tolkien, Unfinished Tales of Númenor and Middle-earth (New York: Houghton Mifflin Company, 1980) 266.