Hello,
If you purchased from Microsoft, you are using digital license.
When you purchased the license, did you purchase the whole Pro license, or was it an upgrade license to allow you to upgrade from Home to Pro?
Is this the reinstall on the same hardare/motherboard? If so, have you already tried this - 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.