Yes, you can change the domain name for your site.
Changing it involves reworking the license agreement as well as reconfiguring the server and the site itself. There is a fee involved to cover the costs associated with it. That can be paid for here:
Once payment has been made, please let us know the new name as well as a good time to make the transfer over to the new URL.
Please email that information to firstname.lastname@example.org
The site itself won't be down but the control panel and functions within the site will be unavailable for a short while as we reconfigure it.