In order to add someone to your health insurance policy, you must first show an insurable interest. That generally limits the people you can add to immediate relatives such as your spouse, children, or dependent parents and grandchildren. Since there is no legal financial obligation between yourself and your girlfriend, she cannot be added to most health insurance policies. The exception to this might be if you live in a state which recognizes common law marriage or domestic partnerships.
If you live in a state where common law marriage is recognized, you can add your girlfriend to your policy as a spouse. The insurance company must recognize your arrangement if it is honored by law. Even if the law does not recognize common law marriage, you may be able to add your girlfriend as a domestic partner if your health insurer allows. You will have to consult your policy or a customer service representative to determine whether your insurance company honors domestic partnerships unless they are allowed by law in your state, in which case the insurance company has no choice.
Even under common law and domestic partnerships, you will usually be required to have a minimum of a shared residence for a number of years before the partnership becomes legalized. This period could be as little as 4 years, but may range to as much as 10. Once you and your girlfriend have lived together long enough, she will be considered your spouse in the eyes of the law and by potential insurers.
Even once you have met the qualifications to add your girlfriend, you cannot usually do so immediately. Most health insurance plans have specific open enrollment periods. You can only add new people to your policy during this time, and the exact dates will vary from one company to another.