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.
I can't rule that explanation out, but I think it's unlikely in this case: my DHCP server knows the MAC address of all of my machines, uses a static MAC->IP mapping, and doesn't update DNS (which is also static). The IP and hostname (as reported by `hostname`) are always correct; it's just the name as reported in the Sharing preference pane and in Finder from other machines on that network that gets the " (N)" suffix.
The hostname returned from DHCP doesn't affect the computer name in Sharing.
What causes the (2) and such to be appended is if mDNS finds a record for whatever the computer's trying to use. I don't really have an idea for why this is happening for dhess since his laptop itself should be the only device responding to the mDNS query...
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.