How to make DHCP domain name registration work with OS X? On Windows computer that are inside a domain the names are auto registered in the domain DNS when the DHCP assigns their IP addresses. 

This is happening because the DHCP server is configured to dynamically update the DNS. 

The problem is that this is not happening for OS X clients and I suspect that I need to configure something in the client to make it work.

How can I solve this problem?
I believe you need to set the DHCP Client ID in System Preferences > Network > Ethernet > Advanced...