The answer to the question, "In Ohio can you get homeowner insurance if your name is not on the deed?" is both yes and no. This is actually a complicated question with a complicated answer. I checked state law and a number of insurance providers for the answers.
The law provides that the beneficiary of a homeowner's policy must be an owner of the property. Anyone living in the home who is not an owner may purchase the insurance, except renters. The non-owner may not receive benefits in the event the policy has a claim. This is primarily to prevent fraudulent insurance policies and claims. A key note here is that the non-owner must be living in the property at the titled owner's consent and must not be a renter. Renters may protect themselves by carrying a renter's policy, which provides for their personal belongings, displacement and in some instances, policies may cover certain repairs.
Homeowners insurance is desirable but not necessarily required, It is an insurance required by lenders with a lien on the property to protect their interests. It is often wise to carry a policy to protect against disaster or someone being injured on the property. The insurance will provide a level of security to protect the owner of the property and future heirs.
If you are living in a a home owned by someone else, are not a renter, and are looking to protect your personal assets, you are better off paying for a renter's insurance policy, as you are not entitled to any payout from a homeowner's policy. I can't really think of a situation where you would want to pay for another's homeowner's policy unless you are the heir to the property and living with the actual owner who do not have a policy of their own.