Don't worry, it's easily done!
You can view your students' usernames from within your teacher account.
- Open Handouts and log in as a teacher.
- Tap on the class to which the student belongs.
- Tap on 'Students' (tab towards the top right of the screen).
- Tap on the student in question.
- Tap on 'Edit student' (top right of the screen).
- Tap on 'Edit profile'. This will bring up the username for the student in question.