A tutor won’t show up on your list unless you’ve rated them via the feedback form at the end of a lesson. If you did not rate your tutor before, you can do so via your Achievements page 
All Live Lessons Rate Tutor.
Once the tutor’s been rated, you’ll be able to filter your calendar to see only their available slots. Anytime a tutor reaches their quota of lessons for the week or is on vacation, we surface a Fully booked notification next to their name and restrict your possibility to schedule lessons with them for that week. That said, the Fully booked notification is always valid for the current week, so feel free to check out upcoming weeks for free appointments and book them.