Moon icon in the bar at the top - actually it is the status bar. It has the time, cell/Wi-Fi signal strength bars, battery icon/percentage, etc.
The moon icon is Do Not Disturb. You can check it in Settings > Do Not Disturb (DND). Also check what Allow Calls From is set to in the DND settings. If you have DND set to Favorites, and that person is not in your Favorites list, it will show the crescent moon icon next to their name.
Also, were you recently using AirPlay?
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