Members plugin - ask for full name in registration, use email address for username

I am trying to edit the registration form to do the following 2 things, neither of which I can manage:

- I want to get their full name, which I will then use throughout the site. I tried adding in fields for full_name, or even first_name and last_name but it seems the registration form is not setting them.

- I also would prefer to lose the 'username' field and instead use their email address for login, this would make things easier. I can't see how to do that.

I'm already using a custom file for the form, using the MEMBERSHIP_REGISTRATION_FORM definition in wp-config.

Please help! Thanks.