Almost all of that comes down to "Are you registered as your business or as your individual?" Because if you registered as your individual self, then your App Store page is going to end up showing your personal name (and not the name of your business) by the time you receive your first payment from the App Store.
If the name on your developer account is "J. Smith", and not "Smith Widgets", then you're going to see "J. Smith" in the App Store. But by the time you get all of your tax information and everything else entered, even if you start out as "Smith Widgets", you end up as "J. Smith".