Morby means 'MoredecaixRigby'. Morby is not 'real' in the show (Since Mordecai has a crush on Margaret and Rigby may have a crush on Eileen) BUT some fãs like the idea of Mordecai and Rigby being gay. So they made up Morby. :)
Of course Morby's fake! Everyone only made it cuz they think of them as a cute couple. Its kinda weird but I guess this how we react to the most coolest shows we ever watch! :/ OH WELL XD