Solaris has a way to fix this and I just discovered that Red Hat has one too. The RHEL 4 Reference Guide mentions adding the parameter DHCP_HOSTNAME in the ifcfg-eth# files. That will tell the DHCP client to specify a hostname when acquiring an IP address.
Another search led to the use of nsupdate which seems to register a Linux host using Kerberos in the AD so that it can update its hostname on future reboots.
I haven't tested both methods yet, but I will soon and let you know.