Behavior of unavailable/private caller ID

What do I need to do to change how Asterisk reports unavailable caller ID? We have an Asterisk machine with a Sangoma A200 plugged into the PSTN. When a call comes in with caller ID, the name/number shows up properly on our Snom 320/360 phones. When someone calls with caller ID blocked or unavailable, it shows up as “asterisk asterisk” on the phones. How can I change this to display “Private” or “Unavailable” as appropriate?