Note: This was originally posted by an inactive account. Content was preserved by moving under an admin account.
What output node are you using? If it's "Output CSV/Delimited" then you can take the file name from a field on the input pin by selecting Filename (from Field) in the drop down in the Output section. Then presumably you don't want to see a column with the file name within the output, in which case you remove it from the Field Order section of the node.
Here is more complete information on what I mentioned above.