How do I report a change of name or address to Medicare?

To change your official address with Medicare, you have to contact Social Security, even if you don’t get Social Security benefits. Here are three ways you can do this: Update your information in your my Social Security account using the My Profile Tab. (This is the fastest way to update your information) Call Social Security at 1-800-772-1213.

https://www.hhs.gov/answers/medicare-and-medicaid/how-do-i-change-my-name-or-address-with-medicare/index.html