It is a very typy Belgian Malinois. I have a smaller matching one lying next to me right now :-) It was very accurate in the first episode how the dog chewed up all the bearer bonds, that is exactly what I would expect from most of the Mals I've seen. These dogs make terrible pets but they are great to work with.
It IS a Belgian Malinois. You can look it up on breeder's site, who provides two dogs who play "Bear" the dog on Person of Interest. A more simple name some use is "Belgian Shepard Dog", but Malinois is most correct name (NOT same as Dutch Shepard) :)