Users without the abusefilter-view-private permission are not able to see the logs of private filters when browsing to them directly (example). However Special:AbuseLog (without specifying a filter ID) shows every filter that's hit, such that one could put together the logs of a private filter.
If we can't see the logs in one fashion, we shouldn't be able to see it any fashion. This includes specifying a user (example), or a page title. Consequently this would mean the filter title is also not visible in any way, which I think is good. Currently many times we have to make our filter names intentionally broad because the target vandal can see it and know it is for them.
The one drawback here is users without the requisite rights won't be able to tell that a user hit a private filter at all. So say if the affected user reached out for help, only filter managers would be able to help them. Perhaps this would need some community input, but again I think it's logical to assume that since I can't see the logs of a filter when browsing to it directly, I shouldn't be able to piece together the same log manually.