I believe that when Feliks Dzherzhinsky (filthy Chekist [spit]) fell from favor, the square was renamed Lubyanka.
I believe Lubyanka was the name of the KGB prison
Dzerzhinksky's statue stood in front of the Lubianka right up until the implosion of the USSR. He was never purged and the name wasn't changed back until the implosion. The commies there are now trying to return the statue to its place.
http://www.eng.yabloko.ru/Publ/2002/papers/upi-160902.html