Do you mean the Great Goblin of Goblin-town? Tolkien doesn't write much about him. We don't even know how large was the territory that the Great Goblin controlled, though his death at the hands of Thorin & Company enraged Orcs throughout the Misty Mountains. Gundabad was considered to be the capital of the goblins of the Misty Mountains; and I'm guessing that Bolg (son of Azog) ruled there.
The Heart of the Wild, a region guide to Wiilderland and Mirkwood for The One Ring Roleplaying Game, does provide some (non-canonical) details about the goblins and their leaders. It tells of the New Great Goblin (the self-styled Greatest Goblin) who replaced the old Goblin-king after the Battle of Five Armies (a second Great Goblin died in the battle). The book also introduces Gorbol, son of Bolg, who seeks to claim the throne of Gundabad which is up for grabs in the years immediately following the BoFA.