According to the regulation, there is only one "customer," the individual. On a good day, the "business" is nothing but a figment of somebody's imagination.
A banker in Arkansas explained it to me that the name of the sole proprietorship was of no more importance than the owner's nickname and she would have put that in the account title too if he asked her too.

However, as Kaybee says, its the banker in you that wants to verify that this is a bona fide account title. You want assumed name certificates, business licenses, tax certificates, or any other government issued document that indicates this is a legitimate business enterprise.