How to add Studio Display to list of AppleCare devices?

Apple Care+ is tied to a specific device. You don't have an overarching Apple Care+ you can add devices to.

If you want to add Apple Care+ for Studio display, then you need to buy Apple Care+ specifically for the Studio Display: click here-> AppleCare Products - Display - Apple

lubec wrote:

I do have AppleCare for the Studio Display. Just would like to know if I can add it to the list of AppleCare covered devices.

If you have Apple Care for the Studio display then it is covered. As I said, there is no list of Apple Care+ covered devices anywhere you can add it to.

Each device has its own Apple Care+ plan.

If you mean the list of devices that appear under your Apple ID, then you cannot add the Studio Display to that list. The list shows devices you are signed into with your Apple ID, not devices covered by Apple Care+.