N.H. CONST. pt. 2, art. 90 provides:
All the laws which have heretofore been adopted, used, and approved, in the province, colony, or state of New Hampshire, and usually practiced on in the courts of law, shall remain and be in full force, until altered and repealed by the legislature; such parts thereof only excepted, as are repugnant to the rights and liberties contained in this constitution: Provided that nothing herein contained, when compared with the twenty-third article in the bill of rights, shall be construed to affect the laws already made respecting the persons, or estates of absentees.

Moskowitz v. Moskowitz, 118 NH 199 - NH: Supreme Court 1978 states:
A review of the authorities makes clear that at common law a person could adopt another name at will. In the absence of statutory restrictions, one may lawfully change his name at will without resort to any legal proceedings if the change is not made for a fraudulent, criminal, or wrongful purpose.