As long as a client is in the same country as the business and meets the eligibility requirements of that business member, the client is free to book with whom ever they choose.
When a new client registers they remain anonymous to everyone except system administrators. When a client requests access to a business member's appointment book, or books an appointment, or sends an e-mail to that business through the system, it is only then that the client reveals their identity to the business member.
As the owner you set the restrictions and process client requests for access. The system is just like your front entrance. You do not see a client until they knock on your door.