Petition fathers rights to be put onto a birth certificate where mothers refuse

I have experience where the mother has re-fused to put the fathers name onto the childs birth certificate and yet are still able to claim csa with NO dna evidence and if the father wants to prove that they ARE or NOT the father then they are the ones that are left to pay the test costs. I would like to see changes not only to the way of registrating the childs birth where BOTH parents should be named on the certificate to have equal parental responsibilites shared but I would also like to see the way csa determine parentage with only the say so of the mother change and that all costs should be equal between mother and father.what we forget as a society is that women hold all the power for continuing on a pregnacy and the man has no say on that weather he's ready to become afather or not but atleast let them have the parental rights once the child is born.it take two to bring the child into the world and therefore two SHOULD have equal parental responsiblities.