It was fairly progressive of DC comics to include a Martian character in the Justice League way, way back in 1960. J'onn J'onzz's presence certainly helped raise reader awareness of Martian culture and their contributions to crime-fighting and planetary defense. But even though J'onn has innumerable secret identities, he's still known among his fellow superheroes as "the Martian". Many even refer to him by that very name.
J'onn certainly fits the Martian stereotype with his vast strength and cerebral powers. He's even green for cryin' out loud (it would be decades later when Morrison corrected this mistake with his 'white martians', but then applied the strongly negative militant stereotype to them). There have been attempts to 'humanize' him by giving him human girlfriends and fostering an addiction to television and chocos. J'onzz remains the JLA's second-banana alien, behind the more acceptably appearing Superman. But the question for me still remains:
Why does it have to be the "Martian" Manhunter? Sure, there's been a few characters by the name of Manhunter, but why does J'onn require the specific planetary qualifier? Is he unfit to take the mantle of this clearly Earthling-centric title? I sincerely doubt that the Martians refer to their Manhunters as "Martian Manhunters". That would be like the English referring to their muffins as "English Muffins".
I'm a big advocate of having better representation of extraterrestrial and robot characters in comics, but find DC's treatment of the JLA's resident token Martian rather repugnant.