@sumudu That's a very valid question. I think the main sense in which you own it is that it is in your domain (as long as you keep up the rental!). And you can back up everything to your computer. Which means that you can upload it to a different host, still with your domain, if for some reason you don't like Dreamhost any more. And you can even, with a bit more nerdery, host it yourself on your computer.
// @matigo