What is the name of Thorin's elven sword?

Thorin's elven sword is Orcrist. The name is Sindarin for “Goblin-cleaver,” an apt title for a blade feared by the Orcs and goblins of the Misty Mountains.

Orcrist was forged by the Elves of Gondolin during the First Age, long before Thorin's adventure. It was discovered in the trolls' hoard alongside Glamdring, another ancient Gondolin sword that Gandalf eventually carried. The two weapons were closely associated as matching blades.

The goblins called Orcrist “Biter” and recognized it when Thorin's company reached their underground kingdom. Like Glamdring, it could glow with a blue light when Orcs were nearby. Thorin carried it through much of the quest to reclaim Erebor, and after his death at the Battle of the Five Armies, the sword was placed upon his tomb.

The other options are famous Tolkien weapons but belong to different characters: Narsil to Elendil and Aragorn's lineage, Glamdring to Gandalf, and Sting first to Bilbo and later Frodo.