[olug] noob question

[Jake Churchill]

I'm not a noob but this is a total noob question.  

You know in Windows you can easily change your computer name (basically
what it shows up as on a network)?  How do you do that with Linux (SuSE
9.2 to be exact)?

Maybe that's not what I really want to ask.  So, here's another one.  At
school if I want to ssh into a machine, I type the server name.  Java
class was java.ist.unomaha.edu.  I know the machine is local but if I
type that either inside or outside the network, I get where I want to
go.  Currently, when I want to ssh into my server, inside my network I
use 192.168.1.103 and outside I use xx.xx.xx.xx (different from inside).
How do I set the name on my machine so it is broadcast?  

To make a question really long, I want to type mycompname.mydomain.com
from ANYWHERE and get to my server.  

So, how do I do that?