Booking tool for psychologist consultations with anonymous option needed

I run a small private psychology practice and want to replace the current back-and-forth over messenger with a proper booking page on the site. Right now, to reserve a session, a person has to introduce themselves and explain what they need help with before anything gets confirmed, and that stops people before they even try, especially when the topic feels personal. I need a specialist who can design and build a booking flow that removes that barrier while still giving me what I need to prepare for each session.

The core idea is an anonymous option: a client reserves a slot under a nickname or initials, with no requirement to state a real name or the reason for the visit unless they choose to share it. At the same time they pick a session format, video call, audio call, or text chat, and see my actually open time slots instead of me updating a spreadsheet by hand. Any notes a client leaves must stay separate from contact details and visible only to me, stored so a leaked database could never tie a topic to a real identity.

Things to plan for:
— a calendar synced with working hours and manual blocking of busy time
— reminders by email or messenger that never mention the topic in the notification text
— an admin view where bookings are visible but anonymous clients stay anonymous unless they add contacts themselves