When I use an instance of a component in another component, to enable its settings in the right menu, I add display properties of the component instance. At this point, the settings group is named the same as the layer in the layers list. If I rename the layer, I will see in the right menu that the name of the property group has changed in the right menu. It works well as long as I'm inside the same file.
If I publish a component with such a renamed layer, then the first time I install it, I will see the correct display of the layer name. But as soon as I change the option in the child instance of the component, and then update the child component's wizard, the layer name resets to the initial one. This is only noticeable if the component instance has been modified. If we reset all the overlays, we will see the correct layer name again.