If you have practitioner booking notifications turned on (such as calendar booking notifications, online booking notifications, or cancellation notifications), the name of the patient is one of things that's included in those notifications!
If for any reason you do not want the patient's name to show up in these notifications, you can set things up so that the booking notifications will be completely anonymous.
Hide patient names in practitioner booking notifications
Head to Settings, and then Patient privacy:
Tick the box next to Anonymise booking notifications:
When enabled, you will only see the patient ID number in the message. Below is an example of a cancellation notification:
There are several ways to figure out who that patient is if you look within Cliniko—if it’s a cancellation, you can check the missed appointments report. If it’s a notification about a new booking, you can check the calendar, or the appointments schedule report. (If you really like spreadsheets, you can also look up the patient ID number in data exports, such as the “Patients” export!)