This discussion is old, so it is unlikely that this really helps the OP, but it may help someone else.
Creating a shared parameter for filename is one way of doing this, but then that parameter needs to be manually updated each time and you are never certain if the filename shown on a plot is really the correct filename. Since I use a version system in my filenames, I really want my filename stamp to ALWAYS and AUTOMATICALLY show the actual filename. But, I don't want the whole file path.
My work around is kind of ridiculous (since it would be far better to just have a real filename parameter built into Revit) but it does seem to work.
I created a plot stamp using a label with the file path parameter. I put this in the bottom right corner of my sheet rotated so it runs vertical and reads from the right. I made it right aligned. It has to extend off the sheet to the left/bottom quite a bit so the whole file path fits without wrapping.
That by itself works, but it leaves text running right to the edge of the page and does not look clean.
I addressed that last problem by creating another label (I just used a second project number label, but you could use whatever-you will need a label with a value in it.) and made the font a almost white (colors 254,254,254) and the background opaque. I put that second label over the file path label so that it cuts it off right where the filename starts. Because it is almost white it doesn't get turned black and doesn't show when plotted. (Since I used the project number, even if it did somehow show, it would at least make sense.)
You will probably have to fiddle with the alignment a few times to get everything just right.
Since my filenames are a consistent length, this works okay for me. If your filenames vary in length, it could still work but would involve more fiddling with the alignment for each project.
Hope that helps someone!