A further solution, which might be just as functional, is to just save the file with a suitable timestamp. The macro below should be called from whichever save function of word that you trap/redirect.
Code:
Sub save_doc_with_pdf_timestamp(doc As Document)
Dim myFullName As String
Dim myFullNameTS As String
' SaveAs2 changes the name of the current document
' therefore we need to preserve the current full name
myFullName = doc.FullName
myFullNameTS = replace(doc.FullName, ".", Format$(Now(), "-yyyy-mm-dd-hh-mm-ss."))
' Saveas2 fails if we don't use the correct file type
' change docx to doc if needed.
myFullNameTS = replace(myFullNameTS, ".docx", ".pdf")
doc.SaveAs2 filename:=myFullNameTS, FileFormat:=wdFormatPDF
' SAVE THE WORD DOCUMENT LAST TO REINSTATE THE FILE NAME.
doc.SaveAs2 filename:=myFullName
End Sub