Hi, Welcome to JustAnswer. I'm a licensed veterinarian and I'll be happy to help. I love the name Dave. . .and through my many years have not run across a cat named Dave! Congratulations to you and to Dave for providing him a home!
Obviously, Dave is uncomfortable without you there, and, honestly, it can take cats quite awhile to adjust to a new environment. There are things to do that alleviate his anxieties, but I'm not sure that getting another cat is the answer. How was Dave in his old environment? Did he tend to hang out with other cats there?
How long have you had Dave in your home?
Could be!!! He's used to feeling safe there!
Since he used to fight with the other cats, he may not be helped by getting another cat. Things that would help him to feel more comfortable when you are gone is first of all time. Cats adjust very slowly to a new environment, so I am glad he has found a safe place, and I am also very glad that he is feeling comfortable with you!
Feliway is a natural kitty pheromone that can calm cats. This comes in a spray or a room disperser. . .you might try this.
Also, leaving the radio or TV on when you are gone can be helpful. When you are home, it is not as dead silent as when you are gone.
Please tell Dave that he is very welcome! One other suggestion to enrich his environment and bring him more peace is to get a kitty tree.
These are great for scratching and climbing, and they also have a perch high up where Dave could lay. Laying up high is also very calming for cats.
Lucky Dave! Sorry that I was away a little bit. . .answering some other questions also.
I really do think that with time, possibly Feliway, a radio left on softly, and a kitty tree that Dave will settle right in to your home comfortably. If he still seems anxious at all in another couple of weeks, we do have anti anxiety drugs available to use on a temporary basis. However, I think you won't need these.