Service and support for your Apple product is linked to its serial number. You can find the serial number directly on your device. If you want to check the service and support coverage of your Apple device, go to the Check Coverage page.
You don't need to register AppleCare+ because it's always automatically registered. You need to register your AppleCare Protection Plan only if you purchase the plan and your covered product separately, or if you purchase your hardware from a reseller who doesn't automatically register the plan. You can register your AppleCare Protection Plan online.
When you go to the Check Coverage or registration page, you can't see who owns an Apple device. You can see that it's registered or covered for service and support.