It does. Sometimes a city might wish only to change the spelling of its name, as when "Hillsboro" became "Hillsborough." But city names have been changed completely in the past, as when Venable became Carrboro or Shoe Heel became Maxton, and the statute permits that sort of change as well. If one of the North Carolina beach towns wants to change its name to Malibu, the statute permits it to do so. (The statute delegates this power to city councils and city voters because a provision of the North Carolina state constitution prohibits the General Assembly itself from enacting legislation that changes a city's name.)