Yes, Medicare provides you with a SEP (special election period) to change your Medicare insurance coverage. Should you plan to move into a different county, contact Social Security @ 1-800-772-1213 (the administrative arm for Medicare) to notify them of your new home address. Your special election period to change your Medicare insurance coverage(s) begins the month of your new move and ends 2 months after your move.
Medicare Advantage plans and stand-alone drug plans are all regionalized so can differ by region. Medicare supplement/medigap plans are defined by Medicare so do not change by region — however, premiums can differ by region and by insurance company. Make sure to do your homework before you move so that you have time to review the options available in your new region before selecting the coverage that will best fit your specific health/drug needs.