Hi Mary
I would believe that all you need to do is pick a name,and submitt it to the State. (Along with money of course) They should issue you a business license, and with that number you are in business. I would suggest getting a checking account for the business as well, just so as to transfer money into from PayPal and to PayPal. Book keeping wise, it is best to transfer all the invoice payment to you and then send the PayPal charges back to them
I am sure you can be a Sol Proprietor to do business in any state.