If you are a sole proprietor:
You can use your name as your business name.
Your phone number as the business phone number
Your address as the business address.
Your SSN for tax id.
And yes, you will likely get a call asking for information such as annual revenue, type of expenses, years in business, how much you think you will spend per month, what the nature of your business is. I think this is mostly to build a profile.
The approval is based on your personal credit report and any payment history you have with AMEX. If you have had a personal card in good standing with them and your credit score is over 700, you should be good to go.