In reply to Frank4short: Good for you getting a rescue.
The story sounds very similar to one of the rescue dogs I had. He had previously been locked in a crate for much of the time, and having more energy than he knew what to do with would be absolutely frantic and get himself in a proper state. When I got him we tried as you have letting him have the run of the house, and whilst he was generally good, he really suffered from separation anxiety (known trait with his breed) and if he got upset during the day then I would inevitably come home to find something destroyed, for example a complete 3 seater sofa torn into little pieces.
We didn’t want to use a crate, and fortunately got a lot of good advice from people with dogs from the same rescue organisation, so thought I would share what worked for us at least. The first thing was to create an area that was his, we just used a small corner of the living room (which was open to kitchen) where there was walls on two sides and the side of the sofa forming the third side, and moved his dog bed there. It was close to all the action in the house, but at the same time when he went there he was completely left along. Key was making it a positive place for him, he was never sent there, and he just took to it as his spot. We did reduce the area of the house he had access to when we were out a little by closing bedroom doors, but generally let him roam so he could protect his pad, investigate noises, etc. Other thing we realised was the house was really quiet, so we used to leave the radio on in the kitchen so there was some level of background noise. Also made out being alone was no big deal, just leave with no fuss, and come home and act as if he wasn’t there (he would be beyond excited someone was home), and then later once he had settled down then call him over and make a fuss of him. Also we avoided strict routine since he would get upset if it was not adhered to (if we were late or whatever). Some mornings I would get up and take him straight out for a walk, others I would have breakfast first and then take him. Some days come home and feed him straight away, others wait some time. The biggest thing though in getting it to work (and don’t mean to point out the obvious) was loads of exercise, especially in the early days, before he was left alone.
Sounds a lot of hassle (and this is without mentioning his fear of being in cars, hose pipes, puddles, vacuums, sticks, etc, etc, etc) but he very quickly took to things and relaxed into a superb dog. He has lived in numerous houses, and a couple of countries, and is an absolutely brilliant outdoor companion. Some things we have maintained such as him having a corner spot that is his, and the lack of routine (because life does not allow for it really), but generally he is completely unfazed by life.