Renaming an Azure VM

I am looking to rename an Azure VM. I have copied a VM from one subscription to another using this guide:

http://blogs.msdn.com/b/microsoft_press/archive/2014/01/29/from-the-mvps-copying-a-virtual-machine-from-one-windows-azure-subscription-to-another-with-powershell.aspx

This has worked fine and I am happy with the newly created VM in my new subscription. However, the VM has retained the original system's name and I would like to rename this.

By "name", I mean the label that is given on the Azure portal on the following screenshot:

I have changed the host name of the new VM in the hope that it would reflect the change in this list, but to no avail. The DNS and all other settings are correct.

Is there any way I can change this without creating a new virtual machine? Perhaps there is a cmdlet which will allow this name to be changed or a hidden option in the portal?

At this time, there is no way to rename a VM. You could try this as a workaround: Delete the VM while retaining all the Disks that were attached to it. Then recreate the VM with the new name and reattach the Disks that were attached to the original VM.