The Metropolitan Museum of Art = MetMuseum
This one is easy, because the one museum to rule them all, despite its slightly stuffy institutional gigantic-ness, has already set the wheels in motion for the neologizing of its arcane, overlong name: The Met's website is MetMuseum.org. And really, the only reason for not cutting it right down to The Met is because of the Metropolitan Opera, which the second half of "MetMuseum" takes care of quite effectively. Total savings: 17 characters.
Museum of Contemporary African Diasporan Arts = DiasporArts
This rising Fort Greene museum's name is even jarring in its MoMA-ified form: MoCADA. Sounds like something you'd order off the secret menu at an Italian espresso bar, amirite? You also lose the museum's very specific appeal, its hook, because "Diasporan" gets de-emphasized. Put that right up-front with the catchy, conflated DiasporArts, which is definitely not the name of a caffeinated drink, but is definitely an edgy little museum in Brooklyn. Total savings: 29 characters.
Chelsea Art Museum = ChelseaSquare
Firstly, the "Art" is redundant, because Chelsea is already synonymous with art, and so you might as well call it the Chelsea Chelsea Museum (more on this shortly). Secondly, a museum surrounded by galleries will inevitably sound a little less exciting—right across the street there's a gallery called The Proposition for chrissakes, how can the CAM compete with that?!—so the name-shortening should also involve a sexing up. Going with the Chelsea Chelsea Museum idea, we get "Chelsea Squared," which, suffused with some mumbo-jumbo about communal non-profit spaces amidst a sea of commercial galleries and the metaphor of a town square, becomes ChelseaSquare (spaces are also redundant, as SculptureCenter proved years ago). Total savings: 3 characters, two spaces.
The Whitney Museum of American Art = WhitneyAM
Good morning Whitney! Doesn't it feel good to shed some of that excess weight? The sunny new name, which simultaneously stands for "Whitney Art Museum" and "Whitney American," provides much-needed relief from the museum's dark concrete cloud-like Madison Avenue building. It's also short enough that when its second building opens (in theory) in the Meatpacking District, the whole WhitneyAM Uptown-WhitneyAM Downtown distinction won't be too clunky. Total savings: 20 characters.