You can hide it from registration and profile edit then set the fallback within CB > Configuration > User Profile to Email. This basically lets you use CB without username, but no you can't actually completely get rid of it as Joomla requires it.
There is also a formatted name. I don't understand the significance or need for this? Can this be removed/disabled as well.
It's a single field for outputting the formatted name. For example if you've first and last name as the name style then that's 2 fields where is formatted name is 1. It is also used by several plugins for displaying the users name and linking to their profile. Move it to a tab in a not shown on profile position if you don't want to use it.