Gaila's moon was a unnamed moon owned by Gaila in the 24th century.
Gaila was able to purchase the moon from the money he made selling weapons. Quark was jealous of Gaila's ownership of the moon. (DS9 episodes: "Civil Defense", "The Way of the Warrior")
Gaila possessed a lavish home on the moon and also operated a lucrative mining venture there. (DS9 novel: The 34th Rule)
Following General Nassuc sending purification squads of the Palamarian Freedom Brigade after him for his dealings with the Regent of Palamar, Gaila was forced to sell his moon to help pay for the weaponry Nassuc demanded of him. (DS9 - Gateways novel: Demons of Air and Darkness)