What I would like is to be able to do is to use another computer's hostname as an IP address. So that when I ping for example: "ping exodia", it'll return as pinging 192.168.0.3 instead of stating it was an unknown host. On my network are six computers, including myself. There are four windows computers. They can ping any computer on the network with the host name and it'll work. From what I've seen, this can be done on Linux using the DNS server configurations. Yet, on this network, we're all connected to the very same DNS server and the Linux computers cannot ping via a hostname. When I restart my computer to Windows, I'm able to ping the other host computers.

So I'm wondering if the ability on Windows is simply because of the NetBIOS settings, or something is faulty with my DNS configurations.

if you had a nameserver on your network ... it would be work as is.

the problem is that the DNS IS running and i'm connected to it, but it's not registering on my computer.

create forword reverse lookup zone and enable SMB service

I had the same problem in an AD-domain, I had to add wins servers to my samba-configuration.
I believe that if Windows-computers uses WINS then you can't find them by FQDN only NetBios-name - pretty strange?
But that's what I did, added
wins server = 192.168.0.1 192.168.0.2
in /etc/samba/smb.conf