The installation went well, but now my Lightroom annouces itself as Adobe Lightroom CC 2015.
Where do you see this? Describe in detail or show us a screen capture.
What do you see if you go to Help->System Info, what version of Lightroom is shown there?
IIRC LR 6 was release in the early part of 2015 (actually April 21 2015). So if you bought it 2 years ago, 2014, you might of bought LR 5.
LR 6 and LR 2015 are exactly the same program. One is the subscription model and the other the perpetual license stand alone version.
The differences come from how you sign in to the program. The Adobe ID you use to sign in with.
When you first install LR 6/LR CC it shows as CC until you license it with a serial number. Have you done that, yet?
In more detail: LR 6 and LR CC 2015 are the same program, with features being shown or hidden depending on how you license the program. LR 6 is licensed via a serial number. LR CC 2015 is licensed via an AdobeID login that has an active subscription tied to it.
I'd guess you haven't licensed via the serial number, yet, after the install on the new computer.
Or, as JSM points out, LR 6/LR CC has only been available for a little over a year so if you purchased something two years ago then it could be LR 5 and your installing LR 6 is starting as a LR CC trial until you license with a serial number FOR LR 6.
Thank you very much everyone for your suggestions.
Indeed I might have bought Lightroom 5 and through the update plan received Lightroom 6 at some point.
To verify the licensing issue I logged myself out of Lightroon and restarted Lightroom.
It asked me to log in again and then gave me the option to license my software, which I did using my non-subscription serial number.
Still the version information shows that it is Lightroom CC (see below).
Any other suggestions?