I recently had to move an Azure service from one account to another.  Unfortunately, they could not migrate my account, which meant that I manually had to migrate it.  In the case of the service, I had created a cname {name}.mysite.com that pointed to the Azure DNS name ({name}.cloudapp.net).  Lucky me: I was able to migrate the service and then repoint the CName to the same DNS entry with no changes or problems.  But in the case of my blob storage ({name}.blob.core.windows.net) I hadn't created a Cname, which means I manually have to update any reference to anything in blob storage. 

Lesson learned: use CNames for everything in Azure in case you need to transfer accounts, ownership, etc.