After you deploy a website (with the xxx.azurewebsites.net namespace), it is associated with a specific region. To change the region, you need to redistribute. Assuming you have your own DNS name, you can redistribute it with a completely new website namespace and then reassign your DNS. Or ... you can delete the current deployment and then get the same namespace name when creating a new deployment in a different region.
You can have multiple web site deployments, each located in any region that you choose.