Which is the official organization for domain registration

There is also gmail.com.

See "googlemail.com domain for certain countries" for more details.

EDIT

My original answer is obsolete at this time. See Change your primary domain from the Admin console

Thanks Rubén for the heads up!

Unfortunately, you can't do this without having to create a new Google Apps account.

From [this Google Apps article][1]:

You can associate additional domain names with your Google Apps account, as separate domains or as domain aliases for your primary domain. However, at this time you can't change which domain is your primary domain. Your only option for a new primary domain is to create a new account and migrate your data to the new account.

In summary, for you to make DomainB your primary domain and DomainA as an alias you would have to:

• Remove DomainB as an alias from your existing Google Apps account
• Create a new Google Apps account with DomainB as the primary domain
• Migrate your data from your existing Google Apps account to your new Google Apps account
• Delete your old Google Apps account
• Add in DomainA as an alias to your new Google Apps account

Important Note:

If you've already purchased a Google Apps for Business subscription for your current primary domain, you can't transfer your subscription to a new domain name. When you create a new Google Apps for Business account for a new domain name, you will be charged for each user account that you create. If you do not want to purchase Google Apps for Business for two separate domain names, disable automatic renewals on your current account and make the change at the end of your current subscription.

The full steps for this process are:

1. Create a new account with the new primary domain.
   
   Sign up for and create a Google Apps account for your new domain name at http://www.google.com/a/.
   
   The domain name must not be associated with any existing Google Apps account. If it is associated with an existing account, you must remove it before creating the new account.
   
   
2. Migrate your data to the new account.
   
   Use one of the email migration options to transfer mail from accounts in your old domain to your new domain. Export any documents, spreadsheets, and presentations you would like to retain and upload them into your new domain, or share them with a user account in the new domain and copy them.
   
   Note: We do not offer migration options for Google Sites. Instead we recommend that you use one of our alternative methods to perform that function:
   
   1. Create a back up for the content in Docs and recreate the site once you register with the new domain name.
   2. Add the new domain admin as owner of the site and then copy it inside of the new domain.
   3. For those using the Sites API, you can go here for the migration options that are available to you: http://code.google.com/p/google-sites-liberation/
   
   
3. Delete your old account.
   
   Once all of your data has been transferred or backed up, delete the Google Apps account for your old domain. It takes five days for the account to be removed from our system.
   
   
4. (Optional) Add the previous primary domain to your new Google Apps account.
   
   If you want to retain the old primary domain as a non-primary domain with access to your Google Apps functionality, add it to the new account.

[1]: http://www.google.com/support/a/bin/answer.py?answer=54819