Menulet Apps

In general the Activity Monitor gives you the process name. However I don’t have the Networks Preferences menulet as shown in your screenshot, so I can’t say much in that particular case.

With the System’s menulets the process name is a bit different. I can for example open the Wi-Fi menulet with this:

tell application "System Events"
  tell application process "SystemUIServer"
    tell menu bar 1
      tell (first menu bar item whose description starts with "wi-fi")
        perform action "AXPress"
      end tell
    end tell
  end tell
end tell

So, you could try to replace “wi-fi” here with “network”.

Keep in mind that certain System Preferences (for example Network Preferences!) are directly scriptable. That means you can do things without clunky UI scripting. You find the scriptable System Preferences and examples here.