Terminal Server Script for printers

Is there anyway to identify what the name of the client is that the user is logging on from? For example I have computerA and computerB, in a script running on terminal server can I tell if the user is using computerA or computerB. I want to be able to set the default printer based on the computer that they using to log into Terminal Server. I know how to set the default printer I just need to be able to tell what computer they are on. Not every computer has a printer so I want to default to the closest printer to that computer. Any help is greatly appreciated.