To change runner label installed on Amazon EC2

Hi AWS, I have created a new AMI from the existing EC2 instance and launched a new instance and it already has the github self-hosted runner configured on it. The trick here I don't want to follow the steps to install the runner again as it is cumbersome and error prone and I am just interested in changing the label of the runner so that the new runner will be cloned with a different label to avoid rework.

I tried that but in order to do that you need to remove the existing runner and reconfigure it with a new label but the issue is now it removes the old runner. My question is am I doing something wrong or this is not going to work?