This has long been a topic of discussion on these threads and I don't believe there is a law that governs this (though someone from OH may be able to chime in and you could check the uniform commercial code).
To me, it is a risk decision. Some banks allow this, but I have seen where banks have had to reimburse a business (the legal entity) for checks they cashed/deposited for individuals who did not own the business and, therefore, did not have a right to the funds. As you can imagine, the risk can elevate extremely quickly if you allow any individual customer to cash/deposit business checks.
That said, if the business is a Sole Proprietor, the individual and "business" are one in the same and, thus, I don't see a problem with this - except that it becomes difficult to differentiate between Sole Proprietors and other entities, meaning it is easier to just draw a line in the sand and say you don't allow this practice.
Adam Witmer, CRCM
All statements are my opinion, not those of my employer, and should not be taken as legal advice.www.compliancecohort.com