N.Y. PBH Law § 4134

§ 4134. Birth certificate; unnamed child. 1. If a living child has not\nyet been named at the date of filing the certificate of birth, the space\nprovided for the given name of the child is to be left blank, to be\nfilled out subsequently by a supplemental report, as herein provided.\n 2. If a child dies without a given name, there shall be entered in the\nspace provided for the name the words "died unnamed." The parents of the\ndeceased child may submit a supplemental report of the given name of the\ndeceased child. Such report shall be returned to the local registrar and\nthe given name shall be entered on the original birth certificate.\n 3. When any certificate of birth of a living child is presented\nwithout the statement of the given name, the local registrar shall make\nout and deliver to the parents of the child a supplemental report of the\ngiven name of the child, which shall be filled out as directed, and\nreturned to the local registrar as soon as the child shall have been\nnamed. The given name, supplied by the supplemental report, shall be\nentered on the original birth certificate.\n