The judge of probate, the license commissioner or such person or persons not residing at the county seat in which the county courthouse is located and duly appointed by the Commissioner of Conservation and Natural Resources and so authorized by him shall have authority to issue all licenses, resident or nonresident, to all persons complying with the provisions of this article and shall sign his name and shall require the person to whom the license is issued to sign his name on the margin thereof. The person or persons issuing said license shall keep in a book or on specially prepared sheets to be furnished by the Commissioner of Conservation and Natural Resources a correct and complete record of all licenses issued, which record shall remain in his office and be open to inspection by the public at all reasonable times.