Ohio Rev. Code § 3513.131
In the event two or more persons with identical surnames run for the same office in a primary 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. Within twenty-four hours after the final date for filing declarations of candidacy or petitions for candidacy, 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 state-wide general and special elections shall notify the persons with identical given names 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 self for the office the incumbent occupies, the incumbent shall have first choice of the name by which the incumbent 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 shall make the determination. In case of state-wide candidates, or in the 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 director of the board of elections or secretary of state by certified mail at the candidate's address listed in the candidate's declaration or petition of candidacy.
R.C. § 3513.131