How to establish a local network domain name

[Randy]

Hi,

Advance note: this is my first time posting to this group, so please
forgive and educate me on any netiquette errors. I also don't know
where the FAQ is. I'm also very green when it comes to BIND and
the entire DNS system. Please bear with me.

I'm using a Fedora Core 4 system on my company's private network. I'm
probably the only linux system on the network - everyone else is
MSWindoze.  Is it possible for me to establish a domain name for my
computer that will be recognized by any computer inside our company's
private network?

Also, if can piggy-back a bit (and this also may be related), how
does it happen that my computer's IP address in the local network
is 192.168.1.100, while whatsmyip.com reports 64.242.84.254?


--Randy Yates