A small idea, similar to some previous ones but still not identical I think:
Pressing Ctrl + C currently copies the path to the selected item in the results list.
Enhance that by letting Ctrl + C do different actions based on the number of times it has been pressed (for the very same item):
1st time - path to clipboard
2nd time - filename to clipboard
3rd time - file to clipboard
4th time - path to clipboard
For each such keypress, indicate the action at the far en of the statusbar: "path", "name", "file".