Hi,
If you get the <VApp> from the REST API you'll see the list of VMs inside it in a <Children> element.
Each VM is a <Vm> element having a 'href' attribute - you can get the VM by doing GET on this href attribute.
After you GET the VM you'll see a <Link> inside it with rel="edit" - this link should be used for updating a VM.
Basically, you GET the XML body of the VM, modify the VM name attribute and then PUT the modified XML body on the same URL.
You also have to specify a Content-Type header in the PUT request: application/vnd.vmware.vcloud.vm+xml
Regards,
Todor Todorov