What is the name of the hill where Boromir died?

The hill where Boromir died was Amon Hen. In The Fellowship of the Ring, Amon Hen stands on the western bank of the Anduin near Parth Galen, at the northern end of the Falls of Rauros.

After the Fellowship leaves Lothlórien, the group travels south by boat. At Parth Galen, Boromir tries to take the One Ring from Frodo, then quickly regrets his betrayal. While defending Merry and Pippin from an attacking band of Orcs, he is struck by several arrows and mortally wounded.

Aragorn finds Boromir at the foot of Amon Hen. Before dying, Boromir acknowledges his failure and urges Aragorn to protect Gondor. Aragorn, Legolas, and Gimli place his body in one of the Elven boats and send it down the Anduin in a solemn funeral.

Amon Hen is often confused with Amon Lhaw, the neighboring hill on the eastern bank. Their names mean the Hill of Seeing and the Hill of Hearing, respectively; Amon Hen is the hill associated with Boromir's final stand.