The Last Unicorn

In an enchanted forest, a talking unicorn learns she is the very last of her kind. A butterfly reveals that a demonic animal called the Red Bull herded her kind to the ends of the earth. Venturing into unfamiliar territory beyond the safety of her home, the Unicorn journeys to find them and bring them all back.
Upon her journey the Unicorn is captured by the evil witch Mommy Fortuna, and is put on display in Mommy Fortuna's Midnight Carnival. As most of the attractions are normal animals with a spell of illusion placed on them (to wit, a toothless lion for a Manticore, a crippled chimpanzee for a Satyr, and a mere snake for the "Midgard Serpent"), Fortuna uses a spell to create another horn on the unicorn's head that the non-magical carnival visitors can see, as they are unable to see her real form. Fortuna keeps the immortal harpy Celaeno captive as well and acknowledges the dangers of caging such a monster, but deems the risk secondary to the deed's recognition and prestige. While held captive, the unicorn is befriended by Schmendrick, an incompetent magician in the service of Mommy Fortuna. With the help of Schmendrick, the Unicorn escapes, in the process freeing Celaeno, who kills Fortuna and her henchman Ruhk. The Unicorn and Schmendrick later gain a second traveling companion Molly Grue, the careworn lover of Captain Cully (the disappointing "reality" behind the Robin Hood legend).
When the Unicorn nears the seaside castle of King Haggard, supposed keeper of the Red Bull, she encounters the animal, which turns out to be a monstrous fire elemental. At the last moment before her capture, Schmendrick uses his unpredictable magic, and transforms her into a human woman with white knee-length hair. In this guise, the Red Bull is uninterested in her and departs. The Unicorn suffers tremendous shock at the feeling of mortality in her body. While Molly wraps the Unicorn's human form in a blanket, Schmendrick states that the magic, not he, chose the form, and promises that he will return her to normal after the quest is complete.
Schmendrick, Molly Grue and the now-human Unicorn proceed to King Haggard's castle. Haggard is at first unwelcoming, and Schmendrick introduces the Unicorn as his niece, Lady Amalthea. Schmendrick requests that the three of them stay there as members of Haggard's court, only to be told that the only occupants of the castle are Haggard, his adopted son Prince LÃ­r and four ancient men-at-arms. Nonetheless, Haggard consents to lodging the trio, replacing his more competent on-call wizard, Mabruk, with Schmendrick, and setting Molly Grue to work in his scullery.
Amalthea begins to forget her identity and her reasons for coming to the castle, and falls in love with Prince LÃ­r. Caught in her newfound emotions, she struggles with thoughts of abandoning her quest for the sake of mortal love. Haggard confronts Amalthea in private conversation, hinting at the location of the unicorns, yet from the waning magic in her eyes, he has doubts regarding his previous suspicions that she is more than she seems. Meanwhile, Molly is able to learn the location of the Red Bull's lair from a talking cat.
Molly, Schmendrick and Amalthea are joined by LÃ­r as they enter the bull's den, but Haggard attempts to trap them by destroying the way they came in. Schmendrick reveals Amalthea's true identity to LÃ­r after explaining what they are looking for. LÃ­r is unmoved and says that he loves her anyway. This makes Amalthea want to abandon the quest and marry LÃ­r, but LÃ­r dissuades her. The Red Bull appears, but is no longer deceived by Amalthea's human form and chases after her. As LÃ­r struggles to protect her, Schmendrick turns Amalthea back into the Unicorn, but she is unwilling to leave LÃ­r's side. The Bull drives her toward the ocean just as he earlier drove all the other unicorns, but she manages to run away and the Red Bull gives chase. LÃ­r tries to defend her, but is killed by the bull. Enraged, the Unicorn turns on the Bull and forces him into the sea. Carried on the white surf of incoming tides, the other unicorns emerge en masse from the water, causing Haggard's castle to collapse into the sea as they rush past, with Haggard falling to his death.
On the beach, the Unicorn magically revives LÃ­r before departing for her forest. Schmendrick assures LÃ­r that he has gained much by winning the love of a unicorn, even if he is now alone. The Unicorn briefly returns to say goodbye to Schmendrick, who laments that he has done her wrong by burdening her with regret and the taint of mortality. She disagrees and thanks him for having helped to restore unicorns to the world; though she is the only unicorn to feel regret, she is also the only unicorn to know love. Schmendrick and Molly watch the Unicorn depart for her home in the woods.

Question: What is the Unicorn's name
Answer: Lady Amalthea.