Yes, "!!!" is a band name. It's supposed to be pronounced "chik-chik-chik."
People. Please don't name your band something with questionable pronounciation. Chik-Chik-Chik sounds cool. But is every ticket seller and record (I'm showing my age) store clerk likely to know how you pronounce it, or are !!! fans resigned to explaining what the band name is each time they say it? Bands, please don't make your fans feel stupid.
On a side note, I think schwah (upside-down e) is a really good name for a band. People (at least the English majors who make up a plurality of my associates) tend to know how to pronounce the name of the upside-down e, though, which makes all the difference.