This ought to be quite simple. I am often not sure which of my (many) similar pictures is the one I want to use although I know its name from prior editing work. Yes, you will say, the name is in the media thumbnails. No, only part of the name is in the media thumbnails, as my naming hierarchy yields long names. Yes, I can hit ctrl-I over the thumbnail and it will give me an info box. And, again, the box is too narrow to show the full filename without dragging out its right side to widen it. So, a slight PITA.
So, what I am suggesting is to have a wider info box (or one with wrapping of a file name) that pops up, perhaps even when hovering over a media asset.