Your question suggests that your child is not yet born, so you will be unable to obtain a Birth Certificate at this stage in any event.
However, when the child is born and a Birth Certificate is obtained, unless the father has consented to his name appearing on the Birth Certificate, only your name will be declared as the parent. If at a later stage it is decided that the child should acquire the father's surname this can be done by obtaining a Statutury Declaration made before a Solicitor/Commissioner for Oaths.