Ubuntu, Windows and my Linksys BEFSR81 Router

[Hodgins Family]

Good evening!

I'm annoyed.
I'm sure I could figure this out elegantly if I knew where to look.
I don't know where to look.
That makes me more annoyed.

I have 3 computers.
One is running Win98, the second dual boots Win98 and Ubuntu, and the third 
dual boots WinXP and Ubuntu.
They are connected via a Linksys BEFRSR81 router (firmware updated last 
year).
During Windows and Ubuntu installations the router was named as the DHCP 
server...everybody has been gettin' their IPs from this little dude for a 
few years now and through several OS installs.
All are shut off at different times and rebooted in no particular sequence. 
Sometimes one or another is off for days on end.

I might get shot for saying this but life in the Windows side has always 
been simple.
If I find myself with two/all the computers running their incarnations of 
Windows I can find the computers BY NAME in the Network Neighbourhood and 
the DHCP table in the router has appropriate entries under Name, IP and MAC 
address. This happens irrespective of which computer was booted up first, 
second or third...they are just there. And I can send files back and forth 
without problems.

Under Ubuntu life is different. If the Ubuntu computers are started up their 
names DO NOT show up in the DHCP table of the router but the IP addresses 
and MAC addresses do.

This is annoying to me. I've started to use NFS on the Ubuntu machines and 
I'd like to put the mount command in my fstab. Unfortunately playing with 
the mount command (on my client computer) at the command line has taught me 
that I have to use the IP address of the server. Using the name of the 
server machine results in the client complaining that it can't find the 
server. If I use the IP address, all is good. I suspect that this is because 
the server computer name is not in the DHCP table of the router. Even 
nastier the IP handed out to a given computer change if all three were shut 
down and then started up in a different sequence.

I'm looking for some leads here. I know Google is my friend but I'm 
uncertain as to what terms to use.
Please somebody tell me that "Google is my friend" give me some leads?

Rob