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In my ongoing refusal to be the curator of a proper Martian Manhunter fan page, I confess that I don't actually like the alias "Martian Manhunter." In the seminal stories, the hero was John Jones, a police detective who was secretly an alien named J'onn J'onzz. "Manhunter from Mars" wasn't a name, just an alliterative descriptive that served as a title for the strip. Five years later, shortly before J'onn J'onzz co-founded the JLA (suck it New 52,) the alien hero became publicly known to exist and operated under the "Manhunter" alias. The term "Martian Manhunter" cropped up over the JLA years, as a soft rebranding for the super-hero set, but the solo strip remained "Manhunter from Mars" and the character's commonly used alias "Manhunter." Even his pet/sidekick called him that, as the whole super-heroes referring to one another by their secret identities crap didn't get started until Chris Claremont's X-Men redefined the tropes of the genre. The moniker "Martian Manhunter" didn't become common within the context of actual stories until the mid-1980s, by which point the simpler "Manhunter" name had been given to numerous other properties, not to mention Michael Mann's screen adaptation of Red Dragon.
It's understandable and practical, but I still find the name "Martian Manhunter" diminishing, like he's an alternative flavor of a name brand despite being far more popular than any of DC's other unspecified Manhunters. Also, because the "Martian" part is already quirky and clunky, it begs people to read too much into the "Manhunter" part. That said, is there anything more fatiguing than some nincompoop making a supposedly clever observation that's patently obvious to everyone else, with the added abrasion of corrupting the memory of an artifact from a more innocent time with cynical posturing? The Martian Manhunter is too gauche to be gay, and after a comment on the OVC site sent me on an investigation, J'onn appears to be exempted from queer variations on rule 34. There's a little bit of slash fiction out there, but I don't think there's any serious interest in the community to recruit a character quite so on-the-nose as "Manhunter." Well, again, mostly.
Not that's there's anything wrong with that, but here's a Broken Frontier article from 2004 that offers an answer to the question, "Why isn't the Martian Manhunter gay?