Use a translation pattern and set the Calling Line ID and Calling Name Presentation to restricted. CSS of the phone should have access only to the partition of the translation pattern. Translation pattern CSS should have access to the other phones. The doc below is old but should help explain.
http://www.cisco.com/en/US/docs/voice_ip_comm/cucm/admin/4_2_1/ccmfeat/fshosp.html
Brandon