Change your primary domain
When you sign up for a Google Apps, you provide an Internet domain name that becomes the primary domain associated with your Google Apps account. You and your users get account names and email addresses at this domain and you can host your website, built in Google Sites if you like, at this domain.
To change your users' account names to the new domain, add the domain as a separate domain. Then move users from their current domain to the new domain. After that, users can sign in to their services using an account name at the new domain. They get an email address at the new domain (and no longer have their old email address). And they can otherwise use the new account name just like they did their old one.
To get started, see Add users from another domain.
The easiest way to create web addresses at the new domain, such as mail.newdomain.com, or to host your business website built in Google Sites at the new domain, (such as www.newdomain.com) is to add a secondary domain then Customise a Google Apps service address.
Using a mygbiz.com trial domain? If you signed up for a trial domain and want to convert it to a custom domain you own, you can do that without having to create a new account. For details, see Convert a trial domain to a custom domain.