New York Consolidated Laws, Public Health Law - PBH § 4134. Birth certificate;  unnamed child

1. If a living child has not yet been named at the date of filing the certificate of birth, the space provided for the given name of the child is to be left blank, to be filled out subsequently by a supplemental report, as herein provided.

2. If a child dies without a given name, there shall be entered in the space provided for the name the words “died unnamed.”  The parents of the deceased child may submit a supplemental report of the given name of the deceased child.  Such report shall be returned to the local registrar and the given name shall be entered on the original birth certificate.

3. When any certificate of birth of a living child is presented without the statement of the given name, the local registrar shall make out and deliver to the parents of the child a supplemental report of the given name of the child, which shall be filled out as directed, and returned to the local registrar as soon as the child shall have been named.  The given name, supplied by the supplemental report, shall be entered on the original birth certificate.