When Norman was accidentally exposed to the gas it gave him super strength. However, the gas had a side effect. Aside from giving a person super strength it also caused Norman to develop a split personality. One was his normal Norman Osborn persona and the other personality was insane. The insane personality began to call himself Green Goblin. However, the effects of the gas eventually wore off.
Later on Harry Osborn exposed himself to the gas and become the second Green Goblin. However, unlike Norman, the gas did not cause Harry to develop a split personality.
In the comics
In the Ultimate universe the U.S. government hired OsCorp to recreate the Super Soldier serum that created Captain America. OsCorp created a drug called Oz. The Oz drug turned Peter Parker into Spider-Man and turned Norman Osborn into the Green Goblin.
In the television series The Spectacular Spider-Man, the formula was called Globulin Green.