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.
I wonder how Nikki Nimrod Haley’s name would appear on ballot in Ohio primaries
Nimrata Nikki Haley
She can use married name. It's not clear if Ohio should allow her to use middle name because Nikki is not nickname for first name.