You might see this error when you try to activate Office 2016 for Mac:
No Credentials. The system requires that you sign on to a valid account.
This might occur because of a problem with the keychain access tool or the Mac OS user profile. Try these solutions to fix the problem.
Reset your keychain in Mac OS X
See this Apple Support article, Resetting your keychain in Mac OS X and follow the steps.
Create a new Mac OS user profile
From the Apple menu, select System Preferences > Users & Groups.
Select Click the lock to make changes, and type your password. Select Unlock.
Select +, and then fill in the new account information, and then select Create User.
If you're still having issues with activating Office 2016 for Mac, please contact Microsoft support.