In Individual teacher's accounts.

Click on the “Students” tab on your Teacher Dashboard and check the “Edit nickname” box next to the students whose nicknames you'd like to edit. Click on the pink button "Edit Nicknames" at the upper or lower right corner of the page. Enter new nicknames in the text boxes and then click on “Change Nicknames.” Confirm the change on the next screen. If a nickname is already taken, please choose another one. A message confirmation will be sent to you, which you can review in your message inbox on the right of your account dashboard.

Teachers in District, School & Faculty licenses.

If you are a teacher in a school you must ask the school admin account user to enable student account management to teachers if you wish to edit students nicknames in a school or faculty license. See here for info about this. Once this permission has been enabled teachers in school and faculty license can edit nicknames, delete students and change passwords.