I have a customer who has make deposits into two seperate accounts (Mr. Jones DBA ABC Mart) and (Mr. Jones DBA 123 Store). Both accounts have the same TIN. Do we need to fill out Part 1 Section A for both DBA's?

Mr. Jones is one person. You can either complete a single section A listing both DBA names in item 5, or do two separate Section A entries. I'd choose the first option. Use Mr. Jones's principal business address or his home address.