Well, it's 'battle dress' in that some wag hung that emotive title on 'powered exoskeleton with armour'. It is technically true (much like a set of fatigues is battle dress) but it's also just dramatic sounding. The designers may never have called it that but the marketers would.
It's really a protected, powered, heavy duty exoskeleton.
Now, a Pioneer versions for breaching operations would really be 'battle dress' and one could argue that Marines on a ship in a damage control set of battle dress may have to fight in that if boarded, so it could still be battle dress. There is a fuzzy line at that point.
For search and rescue, they might call it a 'SAR exoskeleton' or 'lifesaver suit'. They'd be useful in really toxic or dangerous settings and could help with earthquake rescue or other collapse scenarios as well as fires, floods, and underwater rescues potentially.
A cyberpunkish part of my brain wants to call them 'Frames' or 'Powered Frames' because that's the core of battle dress, Alien movie-style power lifters, and every other variant of a powered exoskeleton, however protected or not.