Facebook groups are for real collaboration, not for people to think you are cool. 99.9% of business and non-profits need pages not groups.
Profiles represent individuals and must be held under an individual name, while Pages allow an organization, business, celebrity, or band to maintain a professional presence on Facebook. You may only create Facebook Pages to represent real organizations of which you are an authorized representative.
In addition, Pages are managed by admins who have personal Facebook profiles. Pages are not separate Facebook accounts and do not have separate login information from your profile. They are merely different entities on our site, similar to how Groups and Events function. Once you have set up a Page within your profile, you may add other admins to help you manage this Page. People who choose to connect to your Page won’t be able to see that you are the Page admin or have any access to your personal account. (from Facebook)
Start here: http://www.facebook.com/pages/create.php
Secure your “username”: Login then go to http://facebook.com/username and choose a username for your PAGE, not your profile (though you should have your name as your profile)