sounds like separation anxiety. You might try using a crate so he has less space; it might make him more comfortable to have less space, believe it or not!
There is a thread here somewhere about how to go about desensitizing a dog to being alone. It takes a lot of work, and very small steps. If you can't find it, let me know, and I will make another post.
Experts tell us that it can take up to a year for rescue dogs to settle into their new homes, sometimes. When they find something they really value (their new family) they are afraid when the people leave that they won't come back. Hang in there. Have patience 🙂
Oh, and try the DAP plug ins. They produce a calming pheremone to relax a nervous dog. You can look online, or find them at some pet supply stores. I have no personal experience with them…I keep meaning to try it...but lots of people have very good reports about them.