The reforged sword received by Aragorn in J.R.R. Tolkien’s The Lord of the Rings is Andúril.
Andúril is made from the shards of Narsil, the sword carried by Elendil during the Second Age. Narsil was broken when Elendil fell in battle against Sauron, and its broken blade was used by Isildur to cut the One Ring from Sauron’s hand. The shards were preserved by Isildur’s heirs.
Before the Fellowship leaves Rivendell, the sword is reforged for Aragorn. Its new name, Andúril, means “Flame of the West” in Quenya. The weapon symbolizes Aragorn’s connection to the kings of Númenor and his claim to the thrones of Arnor and Gondor.
Glamdring belongs to Gandalf, Orcrist is Thorin’s sword, and Sting is Bilbo’s and later Frodo’s short sword. These names are therefore not alternate names for Aragorn’s weapon.