Outlook, Exchange & Office365 allow you set a meeting as private when you create it. While Google calendar supports private events within the Google Calendar Apps - this is not exposed via iOS, and thus can not be supported by Meeting Room. Yahoo and iCloud do not support private meetings at all.
When private events are supported by iOS, the Meeting Room app will display the meeting as "Private Meeting" with the organiser of the event also hidden.
If events are not showing up as private in the Meeting Room app, you should check the iOS calendar to see if the event is flagged as private...
Load the iOS Calendar:
Find the event and tap it to bring up its details:
If the Private flag does not exist, your calendar system does not support private events. If the flag does exist, the Meeting Room App will respect this flag.