If my company has changed insurance, does the new insurance have the right to refuse to pay for a prescription I have been taking for over a year?

Yes, if under the policy terms it is not covered.

Every insurance company has their own procedures, which you will likely find in a large document known as the insurance plan, or group plan. One would have to read that question to find the answer to your question. It is possible that the new insurance company requires a generic brand for your particular drug. If so, you have to go by the plan, or pay for it yourself. It likely is easier to comply than to fight. Either your doctor thinks you need it or not. If it is a Rx, your doctor likely would not write the Rx unless you needed it. Why not just comply, rather than fight a losing battle. Get your doctor to give them the proof they want.

Possibly, as your prescription coverage can change annually with the same or a new health insurer.