Unix machines don't normally broadcast their hostnames across the lan.
That's a peecee-lan thing. If they want your unix hostname to show up in
the peecee-lan listings, then you'll have to have samba installed and
have the smbd and nmbd daemons running.

Then they will broadcast whatever hostname your system has. If you want
to force the hostname to be a certain value, it can be set in
/etc/samba/smb.conf - perhaps that adjustment can be made via some GUI
control if you have samba and friends installed, I'm not sure. But the
file edit works directly

Under the [global] section you can set the visible peecee-lan hostname
like so:

netbios name = MULHOLLAND

Restart the samba services after modifying smb.conf