1. Except as provided in subsections 2 and 3 of this section, no political party hereafter organized and no persons hereafter seeking to nominate any candidate by petition shall use any portion of the name of any existing political party.
2. If a new party is formed for more than one district or county at the same time and with the same provisional party chairman, the same name may be used for the party in each such district or county.
3. Any political party established in a district or county may, by a majority vote of its committee members, authorize the use of its name in other districts and counties, and in the state as a whole.