gedit has this bit of code in gedit-mdi.c which is apparently supposed to set
the name in the window list

- if (GTK_WIDGET_REALIZED (active_window))
- { 
-  gchar *short_name;
-  
-  short_name = gedit_document_get_short_name (doc);
-  
-  gdk_window_set_icon_name (active_window->window, short_name);
-  g_free (short_name);
- }

I stumbled upon it while grepping for users of get_short_name and tried removing
it since docs says that "Most of the time this is a bad idea from a user
interface standpoint. But you can set such a name with this function, if you
like" and didn't notice any difference.

We either should remove it or investigate why it doesn't work anymore.