Yes, I gave all the clinics personal information (name, address, nationality, medical history, phone number, email) since my only privacy concern was identity theft (as opposed to being put on mailing list or having my information sold to third party marketers). I only disclosed my credit card and passport info to Banobagi for payment services (passport info was for VAT refund).
When filling out forms, you could just put down a business address if that's a concern but I was upfront with my medical history since that would be relevant to any procedures.
Good luck with your search!