Why does my dog terrorize the house whe he sees my male fiance leave?

It does sound like a little anxiety, with perhaps some assumption that you aren't worth worrying about in regards to his misbehavior. I would put him outside or crate him with a chew while you clean the house, just so he's out from under foot. You can also put him on an "umbilical cord" leash, of about 6-10 ft, and tie it around your waist while you go around the house. I call it the leash of shame, as I only do that with dogs I absolutely cannot trust to behave themselves when they aren't in line of sight.

The crate is a temporary fix that will just keep him contained for when you can't monitor him. The leash method will be the best option for long term behavior changes, as he will no longer have the option of rampaging all over the house, because you can catch him as soon as he starts doing something. After a week or two, he'll be a lot more calm, and will simply trail behind you as you clean.

Although I could not really find anything online talking about this exact subject, I will throw in my two cents anyway. I noticed that you did not mention spending time with your dog. If you have not tried sitting on the couch together while you pet him, taking him out for a walk, playing with him, etc., I think that giving one of those a try may be worth it.

I am not sure what is causing him to behave that way, but here are my guesses: 1) separation anxiety (like you already mentioned) and 2) lack of closeness between you two. What you have described is definitely separation anxiety, but it is odd because you are still there. I found tons of articles online about dogs experiencing separation anxiety when they are left alone. That is why that, in your situation, this leads me to believe that you two do not share a close bond, and that spending more time with him may help.

It sounds to me like you are dealing with separation anxiety. I do not recommend using physical punishers (such as spraying with a water bottle) to stop the behavior. Remember, the real issue is emotional, and that's what you need to work with. Punishers only make the situation more scarry. Instead, you will want to help your dog learn to relax (emotionally) when your fiance is gone.

Go to YouTube and look up "Karen Overall Relaxation Protocol". That is designed to help dogs to relax over a period of about 14 days. You will need to work with your dog every day. Fwiw, I do not take anxiety issues lightly when I train. Imagine being trapped in a state of a panic attack. It's a terrible place to be emotionally. You might want to consider getting help from a force-free trainer (you can look up one in your area at the Pet Professional Guild website).

Sounds like your fiance is the alpha and when he leaves, your dog sees himself as next. The behavior you describe you say he wouldn't do if your fiance was home, so... I was told to lower my voice when speaking to my dog as women have naturally higher voices, so that he knew I was dominant.