The Balrog faced by Gandalf in Moria is called Durin’s Bane in J.R.R. Tolkien’s The Lord of the Rings.
Durin’s Bane is an ancient servant of Morgoth that survived the destruction at the end of the First Age. It remained hidden beneath the Misty Mountains until the dwarves of Moria dug too deeply and awakened it during the Third Age.
The creature killed Durin VI, the king of Khazad-dûm, which gave it the name Durin’s Bane. Much later, the Fellowship encounters it on the Bridge of Khazad-dûm. Gandalf prevents it from following the others, and both fall into the abyss.
Gothmog is another named Balrog in Tolkien’s wider mythology, but he belongs to the First Age. The creature in the Moria episode is specifically Durin’s Bane, not Gothmog.