Register AirPods
How do I register my Apple products and engrave them
iPhone 14 Pro Max, iOS 16
Question marked as
You don't have to register your AirPods or any other Apple product, it's activated automatically once you start using it for the first time.
Regarding engraving, if you mean by Apple, then you should've requested engraving during purchase, after you've purchased it you can't go back to Apple store and ask for engraving as they don't do it in store.