In V15, because each License Key is bound to the FQDN that was used, the License Key cannot be changed post installation.
As the key is a PBX edition in this case, you will use the credentials located in the email you received with the PBX edition key and release the FQDN from the key in order to use the same FQDN again with the new key....logging in to customer.3cx.com with these credentials.
See this guide for more details:
http://www.3cx.com/docs/fqdn-already-in-use/
Then a backup and reinstall is required:
1) Make a Full Backup of your current installation and make sure you
DO NOT check options "Include License Key Information and FQDN".
2) Move the Backup file to a neutral location so it is not wiped out by the uninstall.
3) Completely uninstall 3CX Phone System.
4) Restart the 3CX Server.
5) Download the latest V15 installer from here:
https://downloads.3cx.com/downloads/3CXPhoneSystem155.exe
6) Reinstall 3CX Phone System and in the Config Tool, select to restore a Backup and give it the Backup you made in step #1.
7) The Config Tool will now ask you for a new License Key and for the hostname for the FQDN if you choose to use a 3cx FQDN, to which you can choose the same as before once released from the free license.
To have avoided all a reinstall you could have simply upgraded your PBX edition license to a commercial one.