@Eugene – that problem was and is still pita ;-)
I wrote a script some years ago for a different purpose–PDF-Export in foreground–that would take always the document's name as export name (including .indd). And since this is presented as a dialog to the user with an editable text field, you can always change the name in the last moment, if you like.
Ah thought as much! Very annoying.
If you like, I could rewrite the script:
1. Using the InDesign document's file name without ".indd"
2. Doing the background process instead of exporting in foreground
Maybe in the evening today.
Now I'm off for lunch ;-)
A script would be handy.
But I strongly feel that the file export for the pdf should copy the file name, not a hangover from a previous file name.