The sword Bilbo finds and later gives to Frodo in J.R.R. Tolkien’s legendarium is called Sting.
Bilbo discovers the small Elvish blade in the trolls’ hoard during the journey described in The Hobbit. He keeps it after the trolls are turned to stone by sunlight. Because the sword is short compared with the weapons carried by Elves or Men, Bilbo names it Sting, a fitting name for a blade used by a hobbit.
Sting later becomes Frodo’s weapon. Its most distinctive magical feature is that its blade glows blue when Orcs or other servants of evil are near. Frodo uses it during the journey to Mordor, and Samwise Gamgee also carries it for part of the story. The sword is sometimes confused with Glamdring and Orcrist, which Gandalf and Thorin respectively take from the same troll hoard.
Andúril is a different sword: Aragorn’s reforged blade, made from the shards of Narsil.