If you purchased from Msft, it would be digital license. You shouldn't have to, and actually don't want to uninstall the license on the old device? What step did you use to remove it on the old device?
On the new device, go to Settings > System > Activation, run the troubleshooter, choose the hardware change option. When it asks you where it is installed on right now, you should choose the old device name. Then click on Activate button. And on the next screen when it asks you where to transfer it to, choose your new device name. See if that does the trick.