In my humble opinion, REM were one of the best bands on the planet from 1981 ("Murmur") till 1992 ("Automatic..."). They are still great live, but I have to concur, on record I now find them "dreary", with the odd exception.
Apparently on one of their albums (I think it's the B-side compilation Dead Letter Office) it's stated that it actually stands for Rapid Ear Movement. But they've never suggested this anywhere else.
They chose the name out of a dictionary, having originally been known as Twisted Kites. They also considered Cans of P!ss. Which is sure as hell a name to top charts with.