In order to change the customer’s billing address without editing the information on previous orders, you will need to create it as a new site and set that as the default. If you simply go into the current site address and change it, it will change the information on past orders.
Here is how to correctly update the address:
Go to the account where you want to update the address, and click on the “Sites” tab
Click “New Site”
Enter in the new site information and click “Save”
The page will update. Near the top of the page, there will be a “Set as Default” button, click on it. If you entered an optional Site Name as shown below, it will be overwritten with "Primary Address"
That is now your default address for all new orders made on the account and the new billing address for the account.