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 Bookings, then scroll to the Mobile app preferences section
Next to 'Display names of users on schedule screens,' click the toggle to disable
Need more info on the Schedule & Bookings?