If you have Original Medicare and move to a different state, nothing will happen to your coverage because Medicare is run by the federal government and is standard across all states.
If you have Medicare Advantage, your plan may not be available in your new location. Medicare Advantage is run by private insurance companies with different networks in different areas. So if you move to an area where your current plan is unavailable, you may need to find a new Medicare Advantage Plan. If that happens, you’ll get a special enrollment period to find and enroll in a new plan.