In an alternate timeline in 2422, Morn's was the recreation facility on Deep Space 9, which was previously known as Quark's.

After the Klingons took over the control of Deep Space 9 and Starfleet left the station, Quark owned his own moon. Morn took over for him and renamed the bar years later.

Julian Bashir mentioned on a rescue mission for Benjamin Sisko in 2422 that Dax, Nog, Jake, and he could have a drink at Morn's after the mission was successful. (DS9: "The Visitor")