One of the world's most enthusiastic explorers of alternate realities is Doctor Odysseus. These are a few of the worlds he has visited and named:
Gaia: The Champions Universe. Alternatively, your homegrown campaign universe if it could be the birthplace of a dimension-hopper named Doctor Odysseus.
Hera: A universe where the most powerful supers got together and created a standardized set of laws that they would enforce on the entire planet of Earth. National governments still exist but their ability to make and enforce criminal laws is restricted. One of their laws is the one requiring every active super to join their gigantic super-team.
Athena: A universe where almost every person on Gaia has an opposite sex counterpart
Thanatos: A universe where almost all of Gaia's superheroes have fallen to a necromantic villain who revived them as undead under his control.
Hecate: Magic is the source for superpowers and superheroes operate in secrecy, memories of witnesses end up erased if they can't keep their mouths shut. Technological advancement is somewhat retarded with no cellphones or even personal computers because demons have a tendency to infest cybernetics.
Hephaestus: Advanced technology is the source for superpowers, producing battlesuits, cyborgs, robots and androids in this vaguely cyberpunk reality where corporations and governments create highly visible and merchandised superheroes as well as plausibly deniable "supervillains" and covert operatives.
Persephone: A reality where the supers of Gaia ended up on the opposite side of the moral fence.
Calliope: A reality that seems to have no native supers or exotic technology, but a certain comic book company is publishing tales of Gaia's supers.
Typhon: A reality where the Stars Were Right and despite the efforts of the superheroes human civilization was mostly destroyed by Lovecraftian horrors.
Kratos: A reality where humanity is extinct but other primates took its place. Among their champions are Shock (the monkey), Furious George, Silverback and Battlechimp Potemkin.
Zeus: A world where innate superpowers only belong to aliens, but many aliens have been attracted to Earth by the surprising number of humans who are gadgeteers/
Nike: A steampunk version of Gaia.
Enyo: A world that seems to copy Athena's past, with Adelphine Hitler, Winifred Churchill and Francine Roosevelt leading their respective nations into their version of World War II. Male Gaian heroes may be annoyed by the blatant sexism with which many will greet them.
Zelus: One of those worlds where the Nazis won World War II
Hippolyta : A world where men have disappeared and women reproduce by magic.
Priapus: A world where superpowered men rule in a polygamous and patriarchal culture. They've been to war with Hippolyta.
Achilles: A world with a single really powerful superhero sent to Earth to protect it from alien intruders. Bad news. You count as alien intruders.
Sisyphus: A world of great prosperity, but all of it fueled by brutal exploitation of its superhumans especially the energy projectors trapped in its power plants.
Ekecheira: Superheroes and villains are performers under contract entertaining the public through streaming video sense by the hovering cameras that follow them. The real supervillains were banished.
Porphyrion: Natives are 9 times taller than normal Gaians meaning Gaians are the size of Porphyrion's action figures.
Iris: is a world plagued by demons which are fought off by magical champions chosen shortly after reaching puberty. 90% of the defenders appear as magical girls even though in their civilian form some of them are boys and men.
Use something where they use the first part of a longer phrase to identify themselves. So, you could use something like The Foundation for Social Justice as the full name. But when they Say “The Foundation” with an emphasis on the “The” it takes on additional meaning to those who understand it. It also gives them some cover when overheard or recorded.
"The Community"
Never intended to become a name, just like the classic name for the Mafia: "La Cosa Nostra" is literally just the phrase "our thing", used to refer obscurely to the crime organisation you're running. In the case of "The Community", it was a case of people involved always providing themselves with plausible deniability and even a veneer of respectability, as they do things on behalf of "The Community".
They don't expect you to pay for protection or anything. They simply prefer you to be a generous donor, providing the community with "necessary funding". They don't try to recruit impressionable young mutants or metahumans, to serve as lieutenants of a street gang. No, they simply welcome them to the super-powered community. And if it ends up with them implicated for, or even involved in, some initial crimes, that's just more evidence that the rest of the world is out to get people like us, and only people in The Community really have your back. The super-"heroes"? They're all just sell-outs.
The Nighthawks (Feist...they were technically assassins but so what)
Manus Nigrum (the Black Hand, from VtM)
the Mockers (also Feist...Krondor's thieves' guild)
SPECTRE
Hydra
the Stainless Steel Rats (Harry Harrison)
not stealing...
the Phantom League
the Sundown Society...their work is at night or in the shadows