The board of commissioners shall, at the first regular meeting after the election of its members, designate by majority vote one commissioner to be director of the department of public affairs, one commissioner to be director of revenue and finance, one to be director of the department of public safety, one to be director of the department of public works, and one to be director of the department of parks and public property, except that upon the organization of a board of three commissioners, but three departments shall be designated, as hereinbefore in section 40:72-4 of this title provided and but three directors voted therefor. Such designation may be changed whenever it appears that the public service would be benefited thereby.

The mayor may be designated director of such department as a majority of the members of the commission shall determine.