(c) Gryph- if you repost this article, please post with a link back to my website.
If your rabbit is unpedigreed, then you can name him or her whatever your heart desires. If your rabbit is pedigreed, however, than that changes the situation a little bit. Before we dive into whether or not you can change your rabbit's name, let's address what a pedigree is.
Your pedigree is a piece of paper (or a digital file) recording your rabbit's lineage and is a useful tool to provide dates of birth, weights, varieties (which is the color and pattern), etc. The pedigree is a document which is not required to be recorded anywhere unless you register your rabbit. This means that your pedigree is only as good as the breeder who provides it. For more information about pedigrees, check out my article, Is a Pedigree Important?
When you get your pedigree, the name of the rabbit which is on the pedigree is required to remain the name of the rabbit for the rest of it's life. You are welcome to CALL the rabbit anything you would like- that's a barn name by the way- but you may not change the name on the pedigree. Now, some breeders allow you to change the name IF it is a tattoo ID (ie Gryph's E46A1 could become Gryph's Fluffy) on the pedigree, but be sure to CHECK WITH YOUR BREEDER FIRST! I like to learn what the new owners named their rabbits and I usually send an updated digital pedigree with the new name on it to simplify things.