Go to Admin → Forums, edit the forum, and tick the groups under Who may read it. Leave it empty and everybody can read it.
It applies everywhere at once, which is the part worth trusting: the forum disappears from the index, its topics stop appearing in search — including their titles — and it drops out of activity, personal streams and the recent topics widget. Somebody who has the address of a topic in it gets a "not found" rather than a "no permission", because confirming it exists is itself information.
🚨 Restricting a category restricts everything inside it. A forum with no groups ticked of its own follows the nearest category above it that has some, and the edit screen tells you when that is happening so an empty set of ticks does not look like a bug.
Site statistics still count posts in private forums. A total moving is not a disclosure; nothing with a name in it appears.