Your auditor needs to understand the legal concept of an "entity." In your example, This Business Inc is a corporation, a form of legal entity. " Business Business is simply a nickname under which This Business Inc does business. The corporation is your customer. The fact that an entity using a trade name other than its own must, in some states, register that fact with a state office (often the Secretary of State's office) does not mean that the trade name has its own separate legal existence.
John S. Burnett
Fighting for Compliance since 1976
Bankers' Threads User #8