DHCP allows the computer to send a computer name to the DHCP server, the server can then dynamically set DNS entries based on the computer name.
DHCP is also allowed to send back a new hostname (the reason why on Mac's sometimes depending on the network you are connected to a different hostname is shown on the command line). What is most likely happening here is that your DHCP server is sending you a new hostname because it is not letting your Mac use its old lease for one reason or another.