A significant chunk of US airline flights are operated by a company other than the one whose logo is on the airliner. It mostly applies to the smaller regional "feeder" names, like United Express (actually operated by Cape Air, CommutAir, ExpressJet, and a bunch of others), and American Eagle (operated by AVAir, Chaparral Airlines, Command Airways, and more).
I have no idea if Gotham plans to actually operate that way, but I'd be shocked if there were actually a legal problem if they did.