In J.R.R. Tolkien’s The Lord of the Rings, the Balrog beneath Khazad-dûm is called Durin’s Bane.
The creature is a Balrog, a powerful being of fire and shadow that survived from the First Age. It awakened beneath the Dwarven city of Khazad-dûm after the Dwarves mined too deeply. The resulting disaster caused the abandonment of the city, which later became known as Moria.
The Balrog killed Durin VI, the Dwarven king, and was therefore named Durin’s Bane. In The Fellowship of the Ring, it confronts the Company on the Bridge of Khazad-dûm. Gandalf fights it during the escape and falls with it into the abyss.
Gothmog is another named Balrog in Tolkien’s wider mythology, associated with the First Age and the fall of Gondolin. He is not the Balrog encountered by the Fellowship.