Official business name for an online business...?

You can use any of the three. What is more important is the ownership of the actual name. You should Trademark the name if it is really going to be your business and the 'website name' is as important as it sounds. This is the chicken or the egg argument, but if someone else Trademarks your name after you become successful, then the burden of proof falls on you in the legal battle that will follow, and that can be very expensive.