I have done all of the suggested actions and I am reasonable confident that the file contects are completely irrecoverabe by running CCleaner wipe function and then Recuva secure deletion.
However, the reference to that deleted file, or filename, continues to exist. Can anyone please suggest how I might rid my drive of these completely so that when I run Recuva the results will be zero rather than a host (1000's) of filenames?
And, please dumb it down to novice level for me.

you just posted this, what ever recover finds do not always mean it can be recovered. You even stated this your self. whats in a file name?

simple answer, eraser. which was already posted to you. So if you are not going to bother to read peoples advice......