said by nwrickert :

Sending the name seems to be a windows kind of thing.

I mostly run linux, with a statically defined IP address, and the router does not know the machine name. But when I occasionally boot to Windows, and use the same static IP address, the router knows my machine name (I use a different machine name under Windows, so I can tell it is Windows sending that).

You might be able to block all dhcp requests in a software firewall. But you would have to assign a static IP to do that. So it isn't very practical when using wireless, since you are often using wireless on networks that you don't control and must depend on DHCP to assign the IP.