Renaming a file

I download pdf files regularly which have filenames all different but with a common word in the filename, e.g., FILE0123.pdf and FILE9876.pdf. I can only replace the entire text of a filename using the renaming rule. In my example, I have to "rename" with pattern "name' which allows me to replace the entire text of the filename. Since the numbers after the word "FILE" are always different, I can't seem to get Hazel to do what I'm trying to make it to do. Is the a feature for example like the old dos FILE*.* feature which would identify anything with the "FILE" in it. I hope what I'm asking makes sense.

Have you looked into match patterns? If not, search the help as they should do what you want.