There are no standard federal laws regarding birth certificates; each state has slightly different laws regarding which names must appear on the certificate, and what to do if the father is unknown or does not acknowledge that he is the father. However, some names, such as the child's, are always listed.
Child's Given Name
A child's first and middle names are selected by the parents. There are generally no laws in the United States restricting what a parent names a child. However, according to Peter Mellencamp and Raymond White, a case regarding a boy named "Adolf Hitler Campbell" has brought up the idea that some names could be a form of child abuse.
Most states allow parents to choose whatever last name they would like for a child, although parents generally pass their surname on to their children. If the parents do not share a last name, they may choose which name they would like the child to have. Although patronymy, the practice of giving a child the father's last name, is common in the United States, it is not required. Single mothers often choose--or are required by law absent an affidavit from the father--to give the child their surname. If there is a conflict between the parents about which surname the child is to have, recourse is generally to have the courts decide, with states like Florida requiring a hyphenated last name.
Birth certificates require the mother's full name to be listed and generally request the mother's original, or maiden, name be listed as well.
The laws regarding the father's name vary from state-to-state. In Massachusetts, for example, if the mother is married, her husband is listed as the father on the birth certificate, even if he is not the biological father. If the biological father wants to be listed, there must be affidavits filed from the mother, husband and biological father. If the mother is not married, no father is listed unless both parents agree by affidavit to list his name.