With all things being equal, married people experience lower insurance rates than single people. The theory is that as a single person, you are more likely to be more reckless as a driver than a married person. As to whether your insurance rates will increase if you add your boyfriend as a driver on your policy, you will need to check with your insurance company. In general, insurance companies do not rate insurance premiums on the amount of drivers. They tend to rate the highest risk driver with the highest risk vehicle. That being said, regardless of cost, if your boyfriend drives your vehicle with any regularity, you should list him as a driver on your policy...especially if he resides in your household. Otherwise, you run the risk of your insurance company denying a claim if he is involved in an accident while driving your vehicle.
If adding your boyfriend increases your insurance rates, you can click here to get a Wyoming auto insurance quote (or an insurance quote for another state) and compare your rates.