Legal Question in Business Law in Ohio

No, it's not a violation of CSPA. You can share the name if the nature of the two businesses are not too similar.

Under Ohio law, it may not be a violation of the CSPA to have the word "company" in the name of a non-LLC or incorporated business. It may be a violation to have the words "Inc." "Incorporated," or any variation of "LLC" if that is not the case.

But make sure your name is still registered with the Ohio Secretary of State. It is a violation of the CSPA to run a business, even under a "doing business as" name, like the one you listed, if you have not registered that name as a trade name or otherwise with the Ohio Secretary of State, and you are dealing with consumers in consumer transactions.