On the "Manage Your Kindle" page at Amazon, you have to call the Kindle something. Amazon just calls it "Bob's Kindle" or "Bob's 2nd Kindle". Boooorrrrriiiinnnnnggg.

Plus, people with more than one Kindle might want a certain one listed first so they don't have to think to much when they're buying books with one click. They're listed alphabetically so that makes it easy to be sure one is listed first always.
ANYWAY. . . . you can change the name there and it will show up on the top of your Kindle home screen. There's a whole thread somewhere of interesting Kindle names folks have come up with given that, when you send a book to a Kindle, there's a message that says "sending to <name of kindle>"
Now, if you meant actually putting the name on the physical device. . . .I don't know of anyone who's done that. . . . . .