When two or more political parties, or when two or more political organizations which are not political parties, or when a political party and a political organization which is not a political party, nominate the same candidate for the same office, such nominee shall forthwith designate, in writing, the political party name, or the political organization name, under which the nominee desires to have the nominee’s name printed on the official ballot for the ensuing general election; such written designation shall be filed with the officer with whom the nomination paper, or certificate of nomination by a convention or caucus, is filed and the name of such nominee shall appear on the ballot in accordance therewith.