To see which of your readers have earned a specific badge, go to Rewards --> Manage Badges.
You will see a list of custom badges that you have created.
Click on the badge name, and then click on the 'Awarded To' tab:
You will see a list of any readers that have earned that badge.
If the list is long and you wish to search for a particular reader, you can use the Search field to enter their name and click on the Go button.