Wi-Fi WPA Network Problem

With all the discussion regarding Wi-Fi security on this newsgroup and
comp.sys.mac.system, I decided that I would implement WPA-TKIP (or WEP
if WPA wouldn't work on my System). After setting WPA up in my Belkin
F5D7230-4 router, I was able to get a Wi-Fi connection to the router
with my TiBook running Mac OS 10.3.9; however, I could not connect to
my other computer(s) by using the computer's name... I get a timeout
with a -36 error message. Other computer(s) on my network are Macs
running Mac OS 9.2.2 connected to router by hard wired ethernet. I am
able to connect via Wi-Fi to other computers on my network by the
computer's name when security is turned off.

Actual Alert is: The Finder cannot complete the operatrion because some
data in "afp:/at/G3%20PowerPC:*" could not be read or written. (Error
code -36).

Eventually I found that I could connect with my other computer(s)
(transfer files, view data, etc) if I used the IP Number (192.168.xx.xx)
of the computer I want to connect to instead of the computer's name. Is
this normal with WPA turned on... or am I missing something?

Which method do most of you use to connect to another computer on your
network... IP Number or the computer's name?

Also... I updated Airport software to v42 which did not resolve the
inability to connect by the computer's name... but the update did give
me a lot more choices of which the additional ones won't work on my
configuration anyway ie:WPA2.

Seems to me that if the computers on the network connect to each other
OK when security is turned off, they are configured properly and should
connect OK with WPA enabled; however... as stated above, using the
computer's name no longer works when security in the router is turned on.

Thanks, in advance for any comments or help with this problem... Jim