Joey's quite right that renaming the export via a script is one way. There is a non-programming method that I think should work as well but requires Monarch (and so DataPump v10).
Project 1: do what you need to do with the report and create your exports. Then move the input file to a subfolder without renaming it.
a. open the input file (I'm presuming it's a well-behaved text file) and create a null model that simply traps every line as a one line detail. Paint fields 254 characters wide, called A, B, C etc, as many as you need to cover the line.
b. define a footer template that traps the special value you are looking for. Duplicate this as an append template. Create a calculated field "key" that in the table if(isnull(fieldfromfooter)=1, fieldfromappend, fieldfromfooter) which ensures that every row of data has this value.
c. Create a summary, key fields "key", A, B, C, etc, no measure. Hide "key", export as a fixed width text file breaking on key value changes naming the file according to the key value.
d. Make the input distribution for Project 2 to be "delete".
It would be much more elegant to do this in a script, but it should still be possible without!