Putting him on birth certificate does now give him parental responsibility, didnt use to but they changed it couple years ago. He could get that anyway of course but would have to go to court and be quite determined.
Before dd started school I decided to change her surname so was the same as ds. She had my last name rather than her dads anyway because he never liked his name so he was gonna change it to mine before we split up. But i changed it no probs cos he has no parental responsibility so was nothing to do with him.
But that is a difficult decision to then leave him off is quite a big thing too.
Sorry thats absolutely no help at all