What is the name of Gandalf's horse?

Gandalf’s horse is named Shadowfax. He encounters the great horse in Rohan after asking King Théoden for a mount, and Shadowfax becomes his swift and loyal companion throughout the later part of the story.

Shadowfax is described as one of the greatest horses of Middle-earth, descended from the famous line of the Mearas, the exceptional horses associated with the Rohirrim. His speed is extraordinary: Gandalf rides him rapidly across long distances, including the journey to Minas Tirith during the War of the Ring.

The other choices are also horse names from Tolkien’s world, which makes this a natural point of confusion. Hasufel is a horse ridden by members of the Fellowship, Arod is associated with Legolas and Gimli, and Brego is Théodred’s horse in the films. Shadowfax remains specifically identified with Gandalf.