The way windows does this is using the NMB protocol, you can run that on linux, and use samba instead of nfs, or even use nfs with it but maybe not as seemless.
Configure your hostname in smbd.conf then run nmbd. Then on your second computer run nmblookup YOURHOSTNAME
That /should/ give you the ip of the first. With samba if you are running nmbd you can then just do mount -t smb //HOSTNAME/share /mnt/samba
I'm afraid I don't know enough about nfs to do it with nfs, but you could nmblookup and then use the ip you get from there, but that's kinda sloppy.