Ah, thanks, that makes sense.
Each application can have a username (in the registration object). That username can't be used to login, but it can be used for display purposes in your application: https://fusionauth.io/docs/v1/tech/apis/registrations/
You could allow people to register/login with email address/password and then let them choose their registration.username for use in the application (you'd have to build a page with a form that would use an API key to let them do so). Now that I think about it, I guess you could do the same with user.username, which is the username they can log in with. So that might be an option.
Anyway, good luck and let us know how things go!