Finally, I sorted it so no action needed.
Hello,
Glad that everything has been sorted out.
To connect your Rank Math subscription to the other domain you personally own, you can follow the steps below:
Step 1: Update to the latest version of Rank Math PRO manually: https://rankmath.com/kb/update-rank-math-manually/
Step 2: Disconnect your account from WordPress Dashboard > Rank Math > Dashboard > Help
Step 3: Reconnect from the same page using the same account you used to make a purchase.
You do not need to remove the free version of the plugin. Everything will be ported over to the PRO version.
Here is a KB to help you along the way as well: https://rankmath.com/kb/how-to-upgrade-to-rank-math-pro/
Hope that helps and please do not hesitate to let us know if you need our assistance with anything else.