When you order a Kindle for yourself, they automatically register it by associating the serial number with your account online (same way you'd register a Kindle without Whispernet access if you just wanted to be able to purchase, like the people outside the US who originally got those old non-3G Kindles).
It's just for convenience in shopping pre-arrival and being able to queue stuff up for auto-delivery when you get it. The Kindle itself doesn't know it's registered until you take it out of the package and turn on the wireless so it can contact Amazon's servers and tie itself into your account details.
Warranty's supposed to follow the Kindle (via serial number), not the original purchaser, unless, perhaps you got one of those special extended ones (I don't personally know how they work).
But if you were to get tired of your K3 and sold or re-gifted it to a friend, then if something happened while it was still under the original 1-year built-in warranty, they should be able to contact Amazon for repair/replacement under it, according to what the general experience on the Amazon Discussion forums has been, as far as I can tell.
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