I am too using my domain as internal domain name.
In internet, mydomain.com resolves to my public IP (Wan interface) by my ISP dns and in my internal LAN, it is resolved by zentyal dns server, to private IP in lan interface.
If you configure your server to present same web contents in internal and external interfaces, users gets same result wen browsimg from internet or from lan.
If
www.companyname.com is not hosted in your zentyal server or network, then you have a problem because zentyal dns wil always be authoritative for companyname.com domain for lan clients.
As a workaround, you can probably register an alternate ip in zential DNS (like w3 o web instead of www) pointing to your external web server.
If you change domain name, i think you will need to join to the new domain all workstations( PDC).