Apple Care + for Apple Watch Ultra 2

If this was a used Apple Watch and the AppleCare plan was purchased by the original owner, then you will not be able to renew it unless the seller transferred the plan to you.

If he or she did, or this was a new Watch purchased from an authorized Apple reseller, then based on what the screen shot says, no, it's not going to renew automatically. It says that you need to provide a payment method. However, I don't trust unsolicited links, which too often are scams, so I would suggest that you go directly to Apple.

Extend your AppleCare+ coverage - Apple Support

and follow the instructions. If you continue to have problems, contact Apple Support directly.

Regards.

I'm sorry, but I'm unclear on what it is you are asking. If you purchased your Apple Watch and AppleCare+ from Apple or an authorized Apple reseller, then the AppleCare policy will automatically be registered in the name you used to make the purchase.

If that does not answer your question, please post back and clarify.

Regards.