If you are conducting business, it is a good idea to legally register the name of that business. You don't HAVE to, but it looks more professional and may help settle any disputes that could arise over your domain name.
You have to report ALL income you receive from any business dealings. Chances are when you're starting out, that you'll be able to offset most (if not all) of your revenue with expenses like hosting costs, computer costs, internet connection, advertising, home office, etc, so it shouldn't make that much difference when you file your taxes, especially in the beginning.
I would recommend to hosting company startups to just start as a sole proprietor and run it that way for a while. After you're comfortable with that, then investigate the possibility of incorporating... you could save alot in taxes that way.