In its default state, users will be able to see the name of users who have made an upcoming booking in a room when they're on the room booking screen:
If you'd prefer to make these bookings anonymous and simply have an unlabelled grey box denote the times for which the room is already booked:
Select Settings from the left-hand menu
Click Features then Bookings
Next to 'Display the names of users on booking screens,' click the toggle to disable
Need more info on the Schedule & Bookings?