What is the name of Aragorn's reforged sword?

The name of Aragorn's reforged sword is Andúril.

Before it became Andúril, the blade was Narsil, forged by the Dwarf-smith Telchar during the First Age. Narsil was wielded by Elendil, who carried it in the Last Alliance against Sauron. When Elendil fell, the sword broke beneath him, but Isildur used its hilt-shard to cut the One Ring from Sauron's hand.

The broken sword remained an heirloom of Isildur's line and eventually came to Aragorn. Elven smiths in Rivendell reforged it before the Fellowship began its quest. Aragorn named the renewed blade Andúril, a Quenya name usually translated as “Flame of the West.”

A common mix-up is calling the reforged sword Narsil. Narsil is the original name; Andúril is the name of the remade weapon. Sting belonged to Bilbo and Frodo, while Glamdring was associated with Gandalf.