I'm sure you are disappointed by having the shop disallowed, and I sympathize. I agree with the other posters who said you did the shop wrong. Despite knowing when you started the shop that two female employees had the same first name, which to me means I would have to clarify the last name, you just accepted a first name thinking "I have a 50/50 chance." You did not follow the instructions.
As to your question "Should I report Ellis Property Management to the BBB for not paying shop that followed the instructions?" NO. You did not follow the instructions. BBB is a CUSTOMER protection agency. YOU are the service provider and Ellis is the customer. You did the job incorrectly. If you reported me for nonpayment after doing the job wrong, my my BBB response would include the details of your failure.
Do yourself a favor and settle for the angry post here on the forum where you can remain anonymous. If your name, address, and phone number is published on the BBB internet site as a failed contractor who files invalid complaints and demands payment for jobs not performed correctly, it could impact your relationship with other mystery shopping clients.