In order to find Peter from PBX (extension, bridge, personal, company, CRM, 365) the 3CX client should be in the foreground either on iPhone, either CarPlay or both - because app needs to be in communication with PBX in order to resolve "Peter" name. Also, you can check in the app CarPlay&Siri menu / Voice commands/ Call the filtering - if you set it only extensions then app will look only for local extensions, ie no contacts, no mobiles.
Regarding number prononciation - it's not app problem, it's Siri-user understanding, app only receives what Siri understood.