yes. The context menu is scriptable. That needs a startup script.
And a selected image or the selected frame where the image is placed can be asked for the file name.
But why do you think you'd need a script for this?
Have the Links panel open and you get the information right away.
Another way to get the file name would be to use a function that is already in the context menu:
Create Static Caption *
The default would be the creation of a text frame holding the name.
* Hm. That's a new function with InDesign CS6, I think. You are talking about CS5.
Without using a startup script with an event listening mechanism one could get the name of a selected image by invoking the Script Label panel. Before invoking the Script Label panel a script that you can start from the Scripts panel or by doing a keyboard shortcut would write the name as label to the selected object.
You would have immediate access to the name and could copy it from the Script Label panel.
I am accessing this script through the keyboard shortcut Strg + # on my German keyboard.
For that I did a special keyboard shortcut set.
I think, that's more useful than showing the name in the context menu.