Well, the answer is "it depends", based on the laws in your country. You can do a small company, that's initially you only. You can name your company whatever you want, but is has the be in one line with your name.
For Apple itself, while registering you need only the address and that's it. Later then, when you're uploading apps and place them in the store for sale, you have to enter some tax number (this is different for the country where you register your account) and declare to apple that you're responsible for what you're doing.