Just done some more testing because I seem to remember that I asked this very same question in, I think, version 7 forums, long long time ago.
Now to confuse the issue and throw in a question.
It’s working for me in 9.5 to drag & drop a midi file into an instrument track and retain the midi file name. But only with some purchased midi files. Other purchased midi files take the name of the instrument track.
I think that the question I asked years ago was “is there something embedded in the midi file itself?”
Maybe a red herring, but maybe worth pursuing.
Neil B