Add a father's name to a child's birth certificate by establishing paternity. Use either an Affidavit of Paternity if this is permitted in your state, or ask a court to order paternity testing.
TL;DR (Too Long; Didn't Read)
Adding a father's name to a child's birth certificate grants him parental rights, but it does not guarantee any amount of custodial time with the child.
Adding a Name to a Birth Certificate
It's almost always the father's name that needs to be added to a birth certificate because birth certificates are often produced from the maternity hospital, so the mother's name is available to staff collecting information.
When might a birth certificate be issued without the father's name? The most obvious circumstance is when the parents aren't married and had a brief relationship some nine months before. The man who fathered the child might not know about the pregnancy, or he might know but not want the financial responsibilities that come with paternity.
In these cases, the mother can add his name to the birth certificate for child support purposes. If mother and child receive state aid, the agency providing the aid often has authority to bring a paternity action in the mother's name.
It's also possible that the man who fathered the child wants his name on the birth certificate but doesn't know how to proceed. State laws differ dramatically regarding how unmarried parents are treated in paternity situations.
Options to Establish Paternity Voluntarily
It's easiest for an unmarried couple to establish paternity voluntarily. In some states, a man can establish paternity by simply signing a sworn voluntary declaration that the child is his. He should also file the statement of paternity with the Bureau of Vital Statistics.
In other states, like California, a child's unmarried parents can agree to sign a "Voluntary Declaration of Paternity." Attending medical providers are legally obligated to give an unmarried mother information on the voluntary declaration of paternity. Both parents acknowledge that the father is the child's biological father in the form. His name is then added to the child's birth certificate.
The only way to add the father's name to the birth certificate is for one of the parties to file a paternity action when the mother and father aren't in agreement. A mother may file such an action if the putative father – the alleged father – denies that he is the father. The putative father can also file an action if the mother denies that he is the father.
The court can order paternity testing. A paternity test compares a child's DNA with DNA from the mother and the alleged father using buccal cells taken from the inside of each party's cheek with a swab. DNA paternity tests are 99.9 percent accurate. The court can order that his name be added to the birth certificate if testing establishes that the man is, in fact, the biological father.