How do I go about having my name as father to my son's Birth Certificate.

Submit an affidavit of paternity to the vital statistics agency for whichever state or country you are in. There may be other requirements, such as the mother's consent, as well. Check with the agency.

Any question on law needs to include your general locale as laws vary by area. The first step would be to have a court declare you as the legal father. Unless the mother signs the Acknowledgment of paternity with you, it would most likely require a court order.

First things First, what does the mother say? Second, if the mother denies the fact you are the father that is when the legal case begins. Just because you think you are the dad does not make it so. Paternity DNA test etc. required by a Judge.