You can easily change the primary domain name for your hosting account. In order to do so, you should go to your SiteGround Customer Area > My Accounts > Manage Account (for the account whose primary domain you wish to change) > Change Primary Domain.
Read carefully the changes that will be made to your account and if you understand and agree to them, tick the checkbox to confirm it. Then type the new domain name and complete the process by clicking on the Confirm domain change button. Please make sure you have typed in your new domain name correctly before submitting it so that you do not need to go through this process again.
Please note that if the new domain name is not registered, you will need to register it first. You can do so from your Customer Area, the Order section.