It would make sense if the first kanji is kawa since uzumaki means whirlpool, or swirl. Maybe the name has to do with water. Actually it might have to do with fish, because Naruto is like a fish sauce or something.

Also i wonder about Uzumaki. Since it means swirl Naruto wears a swirl on his coat but then why do the Jounins and chunnins wear it on their shirts and jacket?