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You need to make sure the kobo is registered with the same Adobe ID that the main ADE (digital editions) is registered with.

If the main ADE is not registered with an explicit Adobe ID yet, return the book, register ADE with your ID, and borrow the book again.

To register ADE (if not already registered), menu/Help/Authorize Computer on ADE2, (Library/Authorize Comptuer on the older more reliable v1.7.2).

To register a dedicated ereader kobo once ADE is registered, connect kobo by usb and in ADE use menu/Help/Authorize Device on ADE2, (Library/Authorize Device on v1.7.2).

If the kobo is a tablet device you may need to follow kobo instructions to register the Adobe ID using the app on the device rather than via ADE.