I'm filing a small claim against a Physician whose company is a Professional Corporation; question is do I name the business or the physician?

The general rule is to sue everyone, but in a contract action you would generally not have any recorse against a non-party to the contract, so who is your contract with, the physician individually or the P.A.?  if  you're suing on a contract between yourself and the P.A., the physician would generally not have any personal liability on that contract.