§ 172-e. Change of name of fire district. The name of a fire district may be changed upon a resolution of the board of fire commissioners of such fire district after a public hearing thereon. Such public hearing shall be held prior to the first day of September in any year. The notice of such hearing shall state the proposed new name and shall be published and posted, and such hearing shall be held, in the manner provided in this article for a hearing upon the establishment of a fire district upon petition. After such hearing and upon the evidence given thereat, the board of fire commissioners shall determine by resolution whether it be in the public interest to change the name of such fire district. If it be so determined, the board of fire commissioners, by an approving vote of not less than three-fifths of the voting strength of the board, shall adopt a resolution establishing the new name for the fire district to take effect on the first day of January of the next fiscal year of the fire district. Within ten days after the passage of such resolution, the fire district secretary shall file a certified copy of such resolution (1) in the office of the town clerk of each town in which such district is situated, (2) in the office of the county clerk of each county in which such district is situated, (3) in the office of the clerk of the board of supervisors of each county in which such district is situated, and (4) in the office of the state department of audit and control at Albany, New York.