The Dwarven kingdom beneath the Lonely Mountain in The Hobbit is Erebor.
Erebor is the Sindarin name for the Lonely Mountain, and it also identifies the Dwarven kingdom and stronghold established there. King Thrór founded the restored realm after the Dwarves came from the Grey Mountains. Erebor became famous for its wealth, craftsmanship, and the great hoard that attracted Smaug.
Smaug seized the mountain and expelled its inhabitants before the events of The Hobbit. Thorin Oakenshield then leads a company of Dwarves, accompanied by Bilbo and Gandalf, to reclaim the kingdom. The confrontation with Smaug and the Battle of the Five Armies determine Erebor’s future.
Moria, also called Khazad-dûm, is a different Dwarven realm beneath the Misty Mountains. Belegost is another ancient Dwarven city from Tolkien’s wider mythology. These names are related to Dwarven history but are not the kingdom identified with the Lonely Mountain.