Ohio Rev. Code § 3705.13
When a legal change of name of a person whose birth occurred in this state has been granted by a court, the office of vital statistics shall receive and file a certified copy of the court order legally changing the name. The court order shall be cross-referenced with the original birth record and the office of vital statistics shall issue a certification of birth containing the new name. Such certification shall disclose information that a legal change of name has been granted by a court.
Provided, if the original birth record was filed prior to the establishment of the division of vital statistics, a certified copy of the court order legally changing the name shall be received and filed with the probate court of the county wherein the birth occurred, instead of with the office of vital statistics. The court order shall be cross-referenced with the original birth record and upon request the probate court shall issue a birth record containing the new name. Such record shall disclose information that a legal change of name has been granted by the court.
R.C. §3705.13