The name of the dwarf kingdom under the Lonely Mountain was Erebor. Erebor is the Sindarin name for the mountain and, by extension, the Kingdom under the Mountain established there by Durin’s Folk.
The kingdom was founded by Thráin I after he discovered the Arkenstone, the great jewel later called the Heart of the Mountain. Under the Dwarves, Erebor became a wealthy stronghold rich in gold, gems and mithril. The nearby town of Dale grew alongside it, creating a prosperous alliance between Dwarves and Men.
The dragon Smaug invaded Erebor, drove out its inhabitants and claimed the treasure hoard. Thorin Oakenshield later led an expedition to reclaim it, with Bilbo Baggins serving as the burglar. After Smaug’s death and the Battle of Five Armies, the kingdom was restored. Erebor is often confused with Moria, or Khazad-dûm, another famous Dwarf-realm located beneath the Misty Mountains rather than beneath the Lonely Mountain.