Korgano was the mythological moon god of the extinct D'Arsay civilization.
He existed in counterpart with Masaka, the D'Arsay sun Goddess. Korgano was considered a more benevolent figure than Masaka; he was her nemesis, the one who controlled Masaka and made her vanish from the sky. The exchange of night and day was referred to as "The Hunt".
In 2370, the USS Enterprise-D encountered the D'Arsay archive which downloaded information into the Enterprise-D's computer and began reconfiguring the ship, replicating a D'Arsay city. It also affected Lieutenant commander Data who began taking on personalities from D'Arsay mythology including Masaka. The changes threatened to completely take over the ship until Captain Jean-Luc Picard correctly hypothesized the relationship between Korgano and Masaka.
When questioning the personality of Ihat about Korgano, Picard was informed by Ihat that he had no idea where Korgano had gone, only that Korgano had stopped chasing Masaka for some reason.
Picard used his knowledge of similar legends from other cultures to assume the identity of Korgano and attempted to direct the archive to release his ship. In the character of Korgano he confronted Data, as the archive's representation of Masaka, in Masaka's temple and successfully convinced Masaka to rest. This completed the legend that the archive was enacting and shut it down. (TNG: "Masks")
Korgano was named by writer Joe Menosky after musician Billy Corgan of the band The Smashing Pumpkins. Menosky explained that they were one of his favorite bands at the time of writing the episode. (Star Trek: The Next Generation 365, p. 341)