I do have a Facebook account and I did provide my real information, because--as Sterix said--that information is readily available in a multitude of places. I do have my Facebook privacy set--I forget--probably moderately high.
My primary reason for Facebook, though, isn't music. Because so many people use it, Facebook is a convenient venue for planning reunions (family, class, and others), and I use it mainly for communication with private groups for news (births, deaths, marriages, divorces, graduations, travel plans, and whatever else people can think of) and reunion planning. I manage three family groups and one other social type group (of people who were part of a college-prep program for disadvantaged 10th-grade students in 1966 through 1968 and who bonded with each other and like to keep in touch...and have reunions).
I do have a music page, as well. I figure I might as well since I have an account anyway. I don't market much on it, though, so it doesn't result in much activity. But a little.
I think Facebook is fine for the way I use it, as long as I pay attention to its shortcomings. Nothing is perfect. For music, I use BandCamp and SoundCloud mainly. And CD Baby for distribution.