So you can't rename an Azure VM as this is immutable but you can delete the VM (leaving the disks, network etc) and then navigate to the disk and choose the Create VM option and specify the new name.

Here you can see a vm-vneta is a normal vm. vm-vnetb was originally named vm-netb and I have recreated it using the original disk and you can see by the "SOURCE" column it says "Disk"