DHCP protocol supports sending the client host name to the server via the DHCP HOST NAME option.
See RFC2132 appendix and the original
DHCP Vendor Extension at RFC1497

Further info on the option structure is in the bootp documentation:

You can configure it

On debian:
uncomment the ‘send host-name’ directive in /etc/dhcp3/dhclient.conf

In RHEL:
add the following line to the interface with the ip you want to associate

vim /etc/sysconfig/network-scripts/ifcfg-eth0
DHCP_HOSTNAME=your-nice-hostname