Greetings.
Paul-Robert from Technical Support has closed my former thread about this: http://forum.bitdefender.com/index.php?showtopic=59811
I have now got an answer from BitDefender Support Center:
Let me first thank you for your interest in our security solution, Bitdefender.
We are sorry for the delay of our answer and we hope to assist you in a timely fashion from now on.
Kindly be informed that in order to activate and install your Internet Security 2016, you need to create a different Bitdefender Central account using a different email, and install it on your device using this account.
Which means you will have to get a new email-adress if you want to change your BitDefender product. What a joke!! It took BSC allmost a week to find this answer.