Participants register to attend the Google Calendar event via Google Form
Configure a booking form for each doctor like doing it for personal
Create a custom calendar and some time slots
Share the Calendar with the doctor (who will create his own time slots)
Create a form, connect with the created calendar using BC
Customization (set number of patients per slot, time condition,...). Then, they are auto sync.
Now, every doctor have a separate booking Form, that they can share on email, personal website, socials,... but you (the officer) can integrate them (the Forms) into one site (like this Demo) for the management and patients using purposes
With an unlimited bookings plan (recurring payment) with $10/month you (with your single account) can setup the booking forms up for 6 doctors.