Who is the king of the goblins in the Misty Mountains?

The king of the goblins in the Misty Mountains is the Great Goblin. He rules the underground goblin-city encountered by Thorin's company after the Dwarves are captured beneath the mountains.

In The Hobbit, the Great Goblin presides over a cavernous kingdom filled with armed goblins, tunnels, bridges, and underground chambers. He interrogates Thorin and his companions after they are brought before him, accusing them of spying and demanding to know why they have entered his realm.

The Great Goblin is distinct from Azog and Bolg. Azog is a powerful Orc chieftain associated with the destruction of the Dwarf settlement at Mount Gundabad and Thorin's family history. Bolg is Azog's son and later succeeds him as a major Orc leader. Neither is the goblin ruler who confronts Thorin's company in the Misty Mountains.

The Great Goblin's reign ends when Gandalf arrives and kills him during the escape from the goblin tunnels. His followers pursue the company, but the Dwarves ultimately flee toward the High Pass and Rivendell.