N.Y. CONST. art. I, § 14 provides:
§14. Such parts of the common law, and of the acts of the legislature of the colony of New York, as together did form the law of the said colony, on the nineteenth day of April, one thousand seven hundred seventy-five, and the resolutions of the congress of the said colony, and of the convention of the State of New York, in force on the twentieth day of April, one thousand seven hundred seventy-seven, which have not since expired, or been repealed or altered; and such acts of the legislature of this state as are now in force, shall be and continue the law of this state, subject to such alterations as the legislature shall make concerning the same. But all such parts of the common law, and such of the said acts, or parts thereof, as are repugnant to this constitution, are hereby abrogated. (Formerly §16. Renumbered and amended by Constitutional Convention of 1938 and approved by vote of the people November 8, 1938.)

MANOR HOMES v. Sava, 73 Misc. 2d 660 - NY: City Court, Civil Court 1973 states:
Under the common law — which continues in effect despite the statutory provision providing for a change of name (Civil Rights Law, art. 6) — one may use any name in the absence of fraud. (Smith v. United States Cas. Co., 197 N.Y. 420; Matter of Cohen, 142 Misc. 852; Lana v. Brennan, 124 N. Y. S. 2d 136, 137; Matter of Anonymous, 57 Misc 2d 813, 814.)

Affidavit