In our forum, there is a public category for organizational questions, and an internal one:
Of course, choosing the right one is crucial. Unfortunately, after making you choice, there is no visible difference. This is how both cases look like:
I’d like to see at least a lock icon there, probably also the supercategory, as in the popup.
I think that this use case is quite common.
Not really, there haven’t been too many occasions where a top-level and a subcategory had the same name.
What if you renamed it to “Organisation Intern”?
That’s what I have done for now. But in the topic listing, this now shows 
Intern Organisation Intern, which doesn’t look too good.
I’d think that you run into this whenever you have something where both the public and your staff want to discuss – like organizational questions.