The problem is that once the New event fires, the new document is the active
one; and at this point, as far as I know, Word has no record of what was
previously the active document (if any at all). So you'll need to keep track
of it yourself.

On method is to write your own FileNew function --

Sub FileNew()
   Dim pDoc As Word.Document
   Set pDoc = ActiveDocument
   Dialogs(wdDialogFileNew).Show
   MsgBox "Previous was " & pDoc.Name
End Sub

Put this in normal.dot and it will run in place of the built-in command.
Another approach would be to use an add-in, to trap the Window
SelectionChange event - record the active document each time the window
select changes. Neither of these is a particularly elegant solution. Why do
you need to know it?