There is no easy way for changing the the FQDN, this will require reinstallation using your backup (backup without key and FQDN option ticked). This is important, the backup must not include the “licence key and FQDN” of the previous installation, to allow entering a new key and FQDN during restore time.
You will uninstall your instance after you get your backup off of the machine, then release your FQDN from the customer portal.
You can now reinstall using your backup, and when the wizard asks for a key, it will see that there is no FQDN tied to your key and present you with options to select a new FQDN.
Best read the guide linked by @cobaltit to understand the logic behind how it works, and then follow the linked articles about altering your FQDN.