I found that this feature was requested several times and as it was not fulfilled, I add my voice and ask again for displaying file names in filmstrip view.
When You edit thousand of pictures and Your client sends You a photo selection based on file names, it would save a lot of time to see the file names directly and not be having to mouse over and look in the status bar. It would be much better for orientation when scrolling through a huge collection.
If the client is using the Real file name of the image then use the Filter Bar, Text option, to search for it. That way you don't have to scroll through all the images in the film strip or the grid area.
Thanks for the tip. But that needs to switch from Develop mode to Library, search, go back to Develop and then if You need to see the filmstrip, for example, to compare to compare two following images, You must go back to Library and cancel the search and go back.
For searching one or ten files it is ok, but if You need to search 300 from 5000, then it is too clicky ...