Well, I don't think there's a simple way to set the control to display a short name but save the full name, but here's a way that's kinda fun: use the control's tipstrip to hold the full path and use an event structure to switch back and forth between displaying the full path (for editing) and just the file name.
1. At the start of your program, set the tipstrip (using a property node) to the path (converted to a string).
2. Create an event structure.
3. On the event Value Changed for the path control, convert the new path to a string and save it to the tipstrip. Use the Path to Array of Strings function to get the file name from the last element in the array and write the file name to the path control.
4. On the event Mouse Down for the path control, read th
e tipstrip (using a property node), convert it to a path, and write it to the path control.
This way, if the user wants to edit the path, the full path is restored to the control (as soon as the user clicks on the control). After the user enters a new path, only the filename is displayed, but the full path is displayed in the tipstrip when the mouse pointer moves over the path control.
This doesn't handle the user tabbing to the control, but it might give you something to play with.
In the rest of your program, remember to read the path from the tipstrip and not directly from the control.
See the attached LabVIEW 6.1 example.