If you set the Username field to not display on registration CB will still have to give them a username. It does this by falling back to whatever field you selected for it to use. This is configured within CB > Configuration > User Profile using the Username Fallback parameter. It should be defaulted to Email, but if it was changed to Name you could have issues since in Joomla Name is not unique. You'd need a way to make it unique. The best I can suggest is to set it back to Email then use CB Auto Actions acting on onAfterUserRegistration to alter their username to something more unique.
Have added a feature ticket to see if we can further improve the fallback behavior to automatically handle making it unique to avoid these situations.
forge.joomlapolis.com/issues/7331