What is the name of the mountain where the Paths of the Dead begin?

The mountain where the Paths of the Dead begin is Dwimorberg, also called the Haunted Mountain.

Dwimorberg stands in the White Mountains beside Dunharrow and Harrowdale, in Rohan. Its lower slopes include the Dimholt, a dark wood, and the entrance to the underground passage lies at the Dark Door in a rocky hollow at the mountain's foot.

The Paths of the Dead were created by the Men of the Mountains, who later broke their oath to Isildur. Isildur cursed them to remain as spirits until they fulfilled their promise to the heir of Elendil. Their presence made the mountain and passage feared throughout Rohan and Gondor.

In The Return of the King, Aragorn travels through the Dark Door with Legolas, Gimli, and the Grey Company. He summons the Oathbreakers and leads them south through the mountain toward the Stone of Erech, where they help defeat the Corsairs of Umbar. The paths therefore begin at a doorway beneath Dwimorberg, but the mountain is the canonical geographic answer.