What is the name of the finned metal device that radiates heat away from the processor?

This is called a "heat sink", essentially, a metal plate makes indirect (its separated by thermal paste) contact with the heat spreader of a cpu (central processing unit). The concept is that the heat sink is made of highly conductive materials thus conducting heat away from the CPU, quite often you'll find a fan attached to further disparate heat away from the heat-sink. These days you'll alternative cooling methods, the most common alternative is to use watercooling (another topic). GPU (graphic processing units) also have heatsinks.    

4because of my mind tells me to pick 4

There is a paper clip button you click that to add a photo