New York Name Change

My husband was married before. HE had a step son in that marriage. He was four when he and his ex married. He allowed his ex to give her son his name..They just applied for a Social Security CArd in my husbands last name and then the child became that name..The Child has had no contact from his biological parent nor child support no one has questioned this. But nothing legal was done. He said his lawyer said in New York you can change your name legally one time without going to court or doing any sort of legal documentation..Is this true for New York or any other state? This was 14 yrs. ago also. This boy has my husbands name only because they filled out a SS card application and put my husbands name in..Thanks RobinSJ