I had a similar issue that I was able to solve, I’m not sure if this will help your situation. I was using the clone field to clone another flexible content field. In the clone settings I was using Display -> Seamless which would cause it to break this functionality disable/rename. If I switched to Display -> Group it resolved the issue.
I ran into a similar issue where it would not show the Disabled tag. Not sure if this will help or not. For me, I had set up a Flex field in another field group and then I was showing it via a clone field in other field groups. The issue for me was that if I chose Display -> Seamless it broke the disable/rename function. If instead of Seamless I used Group it would fix the issue.
