Why did Michelangelo sign only the Pieta?
Only Michelangelo could answer this question.
Several years ago I read an item that stated that Michelangelo was upset that no one knew he had done the work, so he went in at night and placed his name on her sash. I think this has a true ring to it.
People didn't know who Michelangelo was when he finished the Pieta and therefor assumed or guessed is was another famous sculpture at the time. When word reached Michelangelo he supposedly walked over to the sculpture with hammer and chisel in hand and wrote/carved his name across the band on the virgin Marie as to cease all confusion as to who the real sculpture was. He was known to have kind of an attitude.