Single domain hosting accounts can only host one domain name at a time, however you are not stuck with the domain name you signed up with and the host name of the account does not need to match the domain name you wish to host.
There are two steps to change the domain name you wish to host:
STEP ONE - Point the new domain towards your server by adding DNS records.
You can find the DNS records you need to add in your hosting management dashboard. Go to "Services" and click the "Active" button to bring up your hosting management dashboard. Scroll down to the section that says "Point your Domain Name to your Hosting Plan using one of the options below" and click "option 2" to reveal the DNS records you need to add. Substitute the domain name showing, with the new domain name to give you the DNS records.
Add the DNS records to your domain by going to "Domains > Manage Domain > DNS Management".
If you have not registered the domain with us, you will need to add the DNS records in the panel provided by your domain registrar.
STEP TWO - Park the domain in your cPanel.
Open your cPanel by clicking the "Web Hosting" link in your "Control Panels" section of your hosting management dashboard.
Go to the "Domains" section and select "Parked Domains" or "Aliases" depending on what theme you are using. Park the domain in your public_html folder by adding the new domain name here.
Following these steps will result in both domain names showing the same website. If you would no longer like to host the original domain name, simply delete all the DNS records or name servers pointing the domain name towards your server.