In The Lord of the Rings, the Elf queen who gives the Fellowship gifts in Lothlórien is Galadriel.
After the Fellowship escapes from Moria, Galadriel welcomes its members to Lothlórien, the Golden Wood. She rules the realm jointly with her husband, Celeborn, from Caras Galadhon. Before the travelers depart, she gives each member an individual gift, along with Elven cloaks and supplies for the journey.
Her gift to Frodo is the Phial of Galadriel, a crystal vessel containing light associated with Eärendil's star. Frodo and Sam later use it in dark places, including Shelob's lair. Galadriel also gives the Fellowship wisdom and encouragement, while Celeborn provides boats for their passage down the Anduin.
Celeborn is Galadriel's husband and co-ruler, not the queen who distributes the gifts. Elrond rules Rivendell, and Arwen is his daughter. Galadriel is also the bearer of Nenya, one of the Three Rings of the Elves. The Lord of the Rings was published in three volumes from 1954 to 1955.