You can absolutely change the booking rules of your online booking from, under "Set Up Page" > "Online Booking Forms" and click on “Who can book?”:

This would then have a pop up page in the right hand side, which allows you to change the booking rules as shown below:

Any Visitor - this allows anyone to book using the form

Registered Users Only - Require customers to register an account before booking using this form

List of Specified People - this allows you to choose specific people/customers who can book with you