Ohio Rev. Code § 3505.021
In the event two or more persons with identical given name and surnames run for the same office in a general or special election on the same ballot, the names of the candidates shall be differentiated on the ballot by varying combinations of first and middle names and initials. Immediately after it becomes known that two or more persons with the same given name and surname are to be candidates on the same ballot for the same office, the director of the board of elections for local, municipal, county, general, or special elections, or the director of the board of elections of the most populous county for district, general, or special elections, or the secretary of state for statewide general and special elections shall notify the persons with identical given name and surnames that the names of such persons will be differentiated on the ballot. If one of the candidates is an incumbent who is a candidate to succeed himself for the office he occupies, he shall have first choice of the name by which he is designated on the ballot. If an incumbent does not make a choice within two days after notification or if none of the candidates is an incumbent, the board of elections within three days after notification shall designate the names by which the candidates are identified on the ballot. In case of a district candidate the board of elections in the most populous county of the district shall make the determination. In case of statewide candidates, or in case any board of elections fails to make a designation within three days after notification, the secretary of state shall immediately make the determination.
"Notification" as required by this section shall be by the clerk of the board of elections or secretary of state by special delivery mail or telegram at the candidate's address listed in his declaration of candidacy or petition of candidacy.
R.C. §3505.021