James, when you purchased the license, it was through Microsoft, right?
Did you purchase the Windows 11 Home license, or the full copy of Windows 11 Pro? Or did you purchase an upgrade license to upgrade from Home to Pro?
If you have the full copy of license, meaning, not the upgrade license, 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.