The dog is named Diamond Dog, D.D. for short, and can come with you as a "buddy" on missions, just as Quiet can. He, also like Quiet, is a completely optional buddy and it's possible to never encounter either of them while playing through the game. Some of these are new screenshots while others were put up last week in other news posts. All of them seem to come from video stills.
And a few gifs for good measure.
It is possible for D.D. and other buddies to die. Once they die, they're gone for good. How's that for a bummer ending to this news post?