Hi,
The default "Registration form" web part has this hard coded - it takes the e-mail value and adds it as the user name:
String plainUserName = txtEmail.Text.Trim();
ui.UserName = plainUserName;
So, you need to either modify the custom registration form web part and add this logic or, if you want to enable the users to login under both user name and email, please follow this approach.
Best regards,
Juraj Ondrus