Well, you'll need a business licence after a while for sure, you can start out under the table, but once you start making real money you'll need to file taxes on it, and then you'll need a business licence.
I say just get it running and started first, make a little bit of money, wait till you get consistent decent business, then go full on getting a business licence and filing it under a corporation so that you don't get shafted by taxes.
I'm pretty sure you can register the business in your name as the sole proprietor, however you should get legal advice before you do so, if worse comes to worse I'm sure your parents will help you out, but again all this leads back to you need to start your business to show your parents you got the goods.
like I said before, the best thing you can do after you start making money is seek legal tax advice, nothing is worse then starting a business and having 40% of your profit taken away, a big difference between decent businesses and great businesses is Tax knowledge.