DirectAdmin lets you do that from your main account login. If you don't know how to loog in to your DirectAdmin control panel ask your hosting provider. Once logged in click on Domain Setup and from there click on Change a Domain Name.
You may or may not be able to add another site; that depends on the resources you get from your hosting provider.
If you can't find those links after you log in to DirectAdmin, then your provider may be using a non-standard skin; you'll need to ask them.
Jeff