At the moment, there is not a way to accomplish this within the UI of the Report dialogue, however, you can do this using the Report API which is available in our Early Adopter Community. We do have an open enhancement request for the ability to reference values within the record to provide a unique naming convention of the report outputs, and I will add your request to it. If you decide to try the Report API, please leave your questions and comments in the Early Adopter Community thread.
Hi Gina Fox,
To reference a filed value in report name when batch printing is supported in the latest release of Survey123 3.9. But you still need to use the Report API to change .zip name if desired.
Jody Zheng Liu