No no, the company that registers your domain really isn't as important, because there really isn't much that they do, so long as they are a good reputable co.. All they really do is allow you to register your address and lock it into you, and essentially them, so no one else can steal it away.
Its a one time flat fee for at least a year (or how ever long you choose) so its not like you'll be missing any payments or really have any needs to change who your registrar is. But you do need to make sure they are a reputable company, there have been issue with registrars in the past.
Wiki might give you a better understanding of how registrars work
Domain name registrar - Wikipedia, the free encyclopedia
Again the reason for not using the same companies, is because your registrar essentially has a hold on your url. You can't move it to another registrar without going through the transfer process and no you can't just re-register it somewhere else.
And like I said you aren't likely to have any issues or reason to transfer to another registrar or at least you are a lot less likely to have issues with them than a hosting co. because they really don't do much. They just give you a url. But you might have reason to move hosts poor service, too much downw time ect.
Now say you miss a payment or two, or have a 1-2yr contract and they are suckin' and you want out. If you have your site registered with them as well as hosted and they are demanding your payment then that is were you might get screwed because then they can lock you out of your own site.
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