It would be helpful to be able to double-click the tab or the title in Scenes palette to edit. I think this used to be the norm.
When I choose “rename”, I can only type “invisible” changes. When clicking on the scene name, it switches to whatever I typed (invisibly), and leaves the edit mode. Thus, you can only change scene names while typing blindly. This is a new bug in the latest update.
I don’t remember that you could ever change the scene name by double click on the scene tab.
When I choose Rename in the Scenes window, the lower section of the window opens so I can see what I’m typing unless it was already open. Are you not seeing that?
I have no longer any pre-Google versions of SketchUp installed, but it might be that it was possible back in the times when Scenes were still called Pages and there were no Styles.