It is the vendor of the book that changes the authorization, not the vendor of the eBook reader you are going to use.
For most books (including library books) you can use your generic Adobe ID, which is the default the authorization screen expects.
If you don't have an AdobeID you will need to get one (free).
I think the authorization screen leads you to the right place, or go to adobe.com, choose "Sign In" (near top right), and then "Don't have an Adobe ID".