Once you deploy a Web Site (with a xxx.azurewebsites.net
namespace), it is associated with a specific region. To change region, you'd need to redeploy. Assuming you have a custom DNS name, you could redeploy with a completely new Web Site namespace and then remap your dns. Or... you can delete the current deployment, then grab the same namespace name when creating a new deployment in a different region.
You can have multiple Web Site deployments, each residing in whichever region you choose.