Ohio actually has a law that says if you legally change your name within the last 5 years, it has to be on the petition. In the article it mentions that there is no place for a previous name (dead name in this instance) on the petition, and the Secretary of State’s candidate guide doesn’t mention this requirement at all.
Apparently other trans candidates had their petitions accepted with no problem.
Anyone can run, they just need to include both names if you legally changed name in last 5 years. It's probably past the deadline for petitions like primary though.