EDIT: I apparently completely misread the original question. Sorry! See @outsidecontext’s answer below instead.
Changing the name Picard saves files under is definitely possible – I’ve probably put way too much time into making my own structure ridiculously complex, just because I have a very specific idea of how I want things to be ordered. In your case, though, the change is luckily a lot easier. Open the options window, and go the the “File Naming” page. It sounds like you still have the default naming script, so replace everything in the main text box with the line:
If you have made some changes already that you don’t want to lose, scroll to the end and then work backward until you find the first
/ then figure out if it’s inside a function (look at the parentheses; the line above has the
/ inside the
$if function), and (if it is) either replace everything to the right of the closing parenthesis or (if it’s on the top level, like the first
/ in that line) replace everything after the slash itself with