There was a post over on the main E: D forum requesting a feature to save the current system name into the screenshot name when you hit F10. Sounded like a great idea to me so I've had a bash at writing a little application that can do it for you.
Feel free to give it a go so grab the zip file and run the .exe in it. No installer needed.
Specify the full path to the screen shot directory (for me it's C:\Users\John\Pictures\Frontier Developments\Elite Dangerous).
Do the same for videos if wanted
Tell it where to save the new image (will default to same directory as the source)
Specify the full path to the Journal files
Choose the file type and the name format (there's a small help screen for the expressions it knows)
Confirm if you want to delete the original file(s).
Launch the game.
It's written with VS Express 2015 in VB.net. Any thoughts, enhancements and bugs let me know but please keep in mind I'm not a coder by trade.
The application works by watching the file system in the specified path for the specified file type(s). When an image/video is created the app will lthen find the last system defined in the current netlog file from Elite Dangerous and use that along with the date (or in game or file creation date) to rename the file. Some options existing for choosing different compression types for the images.
N.B. The application will also work for other games and or housekeeping tasks for renaming images or video's (you can copy old images into a directory being watched and it can then use the images original creation date for renaming).