In 2286, the Alliance was commanded by Captain ("Joh") Morith, and led a fleet of warships that attempted to gain access to Earth by convincing the Federation the fleet was led by New Klingons, a peace-oriented faction of the imperial government. (TOS novel: Timetrap) Given that the entire idea of an alliance was a Klingon ruse in this story, this probably wasn't the vessel's "real" name, but one devised to follow that subterfuge.