I think the term "generic" was invented by subscribers to the web, not by MS, but I could be wrong. There was, at one stage, a published list of keys required for the installation, but not activation. These have since become superfluous, as these keys can only install Windows for evaluation or testing for a short time.
It's not possible to activate it unless you enter a genuine key.
As you know, when you upgrade to the free 10 from an activated Windows 7/8.1 PC, you do not get a product key, but the free Windows 10 activation is registered on MS activation servers for your PC instead. This is not "generic/common, but is unique to each installation. For this reason entering a key during a clean install is a bad idea, if done after you already upgraded to register the activation.
Referring to the OP. I am not aware of a common key to activate Windows 10, but I feel sure it would not be coming from MS, so perhaps David should wait for a definitive answer from the Admin.