"CID Name Prefix" in Ring Group is prepended on inbound external calls but not inbound internal calls

"CID Name Prefix" in Ring Group is prepended on inbound external calls but not inbound internal calls.

For example, our Helpdesk receives calls from inside and outside our institution. The Helpdesk phone number is a ring group. CID on external calls to our Helpdesk are properly prefixed with "CID Name Prefix" but CID on internal calls to our Helpdesk is missing the "CID Name Prefix".

I found some similar tickets but nothing exactly matching our issue.