The sword that belonged to Thorin Oakenshield was Orcrist. The ancient Elven blade was found by Thorin in the trolls’ hoard during the journey to reclaim Erebor.
Orcrist was forged in Gondolin during the First Age, long before Thorin’s lifetime. The Goblins of the Misty Mountains called it “Biter,” a name that reflected their fear of the sword. Its companion blade was Glamdring, which was later carried by Gandalf; both swords were discovered in the same troll hoard.
Thorin used Orcrist during the company’s adventures through the Misty Mountains and Mirkwood. In the Battle of the Five Armies, he fought with it before being mortally wounded. After Thorin died, the sword was placed on his tomb beneath the Lonely Mountain. Its blade was said to glow blue when Orcs approached, helping protect the grave from being disturbed.
Narsil belonged to Elendil and was later reforged as Andúril. Glamdring belonged to Turgon before Gandalf, while Sting was the small blade Bilbo gave to Frodo. Those famous swords are therefore not alternate names for Thorin’s weapon.