There is a way to do it with a little script for a dhcp hook as described here.

Create a new file:

sudoedit /etc/dhcp/dhclient-exit-hooks.d/hostname

and paste the following code:

#!/bin/sh

# Filename:     /etc/dhcp/dhclient-exit-hooks.d/hostname

# Purpose:      Used by dhclient-script to set the hostname of the system

#               to match the DNS information for the host as provided by

#               DHCP.

#





# Do not update hostname for virtual machine IP assignments

if [ "$interface" != "eth0" ] && [ "$interface" != "wlan0" ]

then

    return

fi





if [ "$reason" != BOUND ] && [ "$reason" != RENEW ] 

   && [ "$reason" != REBIND ] && [ "$reason" != REBOOT ]

then

        return

fi



echo dhclient-exit-hooks.d/hostname: Dynamic IP address = $new_ip_address

hostname=$(host $new_ip_address | cut -d ' ' -f 5 | sed -r 's/((.*)[^.]).?/1/g' )

echo $hostname > /etc/hostname

hostname $hostname

echo dhclient-exit-hooks.d/hostname: Dynamic Hostname = $hostname

Replace eth0 and wlan0 with the names of the interfaces from which you want to obtain the hostname. In most cases eth0 and wlan0 should stay the same.

Make sure it is readable...

chmod a+r /etc/dhcp/dhclient-exit-hooks.d/hostname

That's all. On the next dhcp response your hostname will update automatically.