Internal vs external domain addressing

[antonio.nunes at lifefoundation.plus.com]

Hi,

On our setup when we want to address our server (used both for email and http) from the internal network we need to address it as "machine.ourdomain.com".
When connecting from outside the network (through the internet) we address the server as "ourdomain.com". How can I configure our BIND server (FC2) so that we can use the 
same address regardless of where we are sending from? Can I make settings so that "machine.ourdomain.com" is recognised on the internet, or do I need to contact our ISP for 
that?

Thanks,
Antonio