What is the name of the Software/set up that allows you to display photos on your laptop while taking photos?

It's called Tethering. Not all cameras have this function, but most DSLRs do. You'll need the cable (usually comes with the camera, one end looks like a USB cable and the other end goes in the camera), and Photoshop (the full version) or Aperture (cheaper if you have a Mac).

There are a lot of companies that make software to tether cameras to a computer. Check with your camera manual or the manufacturer to see if your camera supports tethering and to see if they offer such a program. I shoot Canons and they offer Canon Remote Capture. If you have Photoshop and installed Bridge you can use that also.

If your camera does support tethering you can do it with either a Firewire or USB cable (your manual will say what you have) or it can be done wirelessly (expensive). I use a 15' USB 2.0 cable on mine and it works nice. If you hear a photographer referring to a "monkey leash", that means they are shooting tethered.

This is the one we use in our studio : http://www.breezesys.com/products.htm

It's nice because it has a lot of great functions like reading the buckets and ability to change iso and other settings from the computer