Well, I did use the 'uninstall licence' option on the 'help' menu and started up 3dCoat again.
This time I was prompted for the licence key and the key for the Professional version was accepted. In the attached image you will see that the error is gone and that the version is no longer 'Educational'.
Thanks again, Carlosan. I now have many hundreds of hours work before I will be competent in this wonderful program.