Yes, The New Music has a nomenclature crisis, a branding problem. It doesn't help that we can't unambiguously use The New anymore in the US or other anglophone contexts (unlike in German-speaking countries in which the Neue Musik term still has some charge, almost a century late), at the very least ever since the New Music America Festival days (1979-90), during which time the New Music label got diluted internally by an increasingly diffuse content message (in large part due to a necessary increase in programming diversity, but still diluting the brand name) and was externally occupied by an "alternative" popular music trade fair (but then again, new as in novel was never going to be a useful external label for a particular tradition as each tradition can and will have its own novelty acts.)
I don't have a solution to this. After the New Music, there will always be another New Music. Contemporary Music is supposed to be what's happening now (though usually sounds like what happened then.) I happen to like experimental music, but it's a label about means not ends, too internal to compositional or technical concerns and without much suggestion to potential listeners. I like The Radical Music even more, but for a particular direction of music-making, and I'm a party of one here with regard to the name. So in the meantime, until we can agree on terms, maybe we can just settle on making and listening to, well, music?