Topic

I am about to upgrade the SSD in my macbook and need to know whether to de-register the computer from pScan before upgrading. I will be restoring the software from a time machine backup. By changing the SSD, will pScan think that the computer has changed?

If it is not necessary, then I am aware that I won't be able to re-register the computer again afterwards. 

Thanks for any advice.

The registration is based on the computer hardware. Reinstalling the operating system, or the hard drive should not cause a problem. 
Just change the harddrive, and reinstall everything. 
If anything goes wrong we can sort it out. 

If you are not sure that you will do everything right, you should not do it yourself. If I were you, I would contact https://www.salvagedata.comdata recovery and tell them what requirements you have for their work in this case. I am sure that the specialists from the service center will do the designated work better than if you try to do it yourself. If you want to do everything yourself, you should first write down all the account credentials, logins, passwords, and other credentials to avoid later losing this information.