N.H. Rev. Stat. § 5-C:89

I. Other than corrections in spelling, clerical errors, or omissions, name changes involving the name of the registrant, or the names of his or her parents as listed on a birth record, shall require a certified copy of a court order that states the name to be changed and how the name is to appear on the birth record. II. Within 6 months of the filing of the birth registration, a request to change the spelling or to add the name of a child shall be processed by the clerk of the town or city. The form used to make the request shall be signed by the parent as recorded on the birth record, the guardian, or the legal representative of the registrant and shall be an acceptable affidavit for such a name change. The record shall be noted with the first name, middle name, or last name, as applicable, and "Corrected" and the date. The applicant shall present either a driver's license or other photo identification to the clerk of the town or city when making the request. III. Irrespective of the time elapsed since the date of birth, if the surname on the birth record is blank, the registrant may request that the clerk of the city or town add a surname to the birth record, but only if the surname of the father shown on the birth record agrees with the surname that the registrant desires to add to the birth record. IV. If a surname different than the surname of the father is requested, the amendment request shall require either a certified copy of the court order or the completion of the form described in RSA 5-C:85, II and submission of the documentation by the clerk of the city or town to the state registrar. V. If a request for a change of the child's surname in connection with a court order of legitimation is made, the new surname shall be the name shown on a certified copy of the court order of legitimation and shall appear as such on the new birth record.