Where is this hidden computer name coming from?
The right way to do this is to use a sysprepped image. Barring that, you need to rename your SQL instance(s) after renaming the computer.
https://docs.aws.amazon.com/AWSEC2/latest/WindowsGuide/ami-create-standard.html
https://aws.amazon.com/premiumsupport/knowledge-center/sysprep-create-install-ec2-windows-amis/