Just to be clear, you would like to run an action on a file, say, open, sharpen, resize, etc... and then open another file of a specific name within the same action? Then, the same action would modify that newly opened file? Or are you attempting to alter the names of a batch of files?
Wow, this is a tricky one. I'll need to do a little homework and then respond if I can make any sense of that. It's almost like it's a bug in Photoshop or something. Although, I have seen some crazy workarounds in my day. Let me think about this one. I can imagine how frustrating it is to have the same filename used over and over when that should obviously change as new files are used.