You can directly add the default WP fields for display name and nickname to the form by adding a text field and using the correct meta key for the field (“display_name” or “nickname”). If these fields are in the form, WP-Members will process them accordingly. When they are excluded (such as in a default configuration of the plugin), then they are populated with the the username, since WP requires that these contain a value for every user.
As for removing the username field, I recommend that you not do that. I understand that you want to have this be the email address, but that can be problematic. It is much better to have a user login that does not contain special symbols (such as “@”). The username is the WP user_login, so it is required that it be populated with a value, and in many cases, emails can be used for this. But there are many issues that arise with that because (1) WordPress does not allow a mechanism for changing usernames for a user, so when they change their email address, now you have a problem and (2) installs such as multisite or certain other plugins use the username value for other things and the “@” symbol becomes an illegal character. The plugin and WordPress both allow for login using either the username or email address, so it is not necessary to create a username from the email address.
