what type of field do you want and what for?

to create the field is easy, but to use the information on it will need more code to do.

The easiest way i find to achive it is to rename the "Nick" field with "Domain name" so everytime a user want to request a chat, they must identify themselves as the domain name

as I told you, you'll need to "scratch" the code, otherwise you can use the other solution

if you get the code of how to do what you want, please share it here

That's something on the board for 3.0, the ability to define input fields on the chat initiate screen.  Right now it's rather tedious, since you must define a variable, process the request and assign the value to a PHP variable, and export the variable to the template system, and finally add code to the template to show the variable.  Yes, I know it's convoluted, that's why it's being changed...