I would imagine that the chance of getting sued is quite small. What individual would sue and what harm would they claim? Government FTC most likely would not care and if they did all they would have to do is change the picture.
Likewise if there was an accident someone would have to say they relied on that information and was mislead. Unlikely (especially in the case of death how do you prove that?). Plus it is common practice to operate like this by similar parties.
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.
Likewise if there was an accident someone would have to say they relied on that information and was mislead. Unlikely (especially in the case of death how do you prove that?). Plus it is common practice to operate like this by similar parties.
Here is a similar company for jets:
http://www.bluestarjets.com/
Note how they do the same thing but don't have any logos on the jets.
http://www.bluestarjets.com/?page=company-payment-legal
My guess is that the "Gotham Air" will disappear from the home page picture.