Wi Fi identifier / name

Hey, well I searched all the forums first. But I did not find the right answer.

When I go to the Administrative page for my 2Wire ATT wireless modem, and I click on 'Home Network' ,
It will show all the devices that access my 2Wire wireless modem/router.
It shows all the ones that are actively accessing my modem and the ones that have in the past but are not on, or are not active.

So I know that I can give devices a name from the 2wire home page. But some of the devices (computers) already have a name.

So the main question I am asking is , is there a way to give your computer a name that will be recognized by the modem/router? Is there a way to do it from the computer side, and not from the modem admin. side.
There must be. I have done it in the past.
I think there is I just can't remember right now.
Can anyone help?
Thanks

(I have an iMac Power PC G5 with 2G Ram) Running Tiger 10.4.11 "It's Maxed out"