This can be done through a Registration ReportWriter report. 
  1. Go to Data Management > select Reports
  2. Select the Report Writer tab
  3. Click Create a New Report
  4. Select TeamRaiser from the drop down
  5. Click the Registrations radio button
  6. Click Next
  7. Under the Discount Information section, mark Discount Name and Discount Code
  8. Select other fields you want to include
  9. Click Next
  10. Follow the on screen prompts until you get to step 5, Configure Filters
  11. Click Edit next to Event is any of the following
  12. Click Select
  13. Select your event
  14. Click Save this filter
  15. If desired, you can remove the Registration Active Status filter by clicking the trash can icon. (Note: If you want to see who has used a specific discount code, filter it by selecting Discount from the drop down menu at the top and then Discount Code (or Discount Name) from the second drop down).
  16. Follow the on screen prompts to save and/or run the report