The idea of having a date/time field is good .... create a workbook smilar to this
add the following code to the ThisWorkbook module:
Private Sub Workbook_Open()
If [B2] = "" Then
' timestamp
[B2] = Now()
' suppress warning when saving macro containing workbook in non-macro format
Application.DisplayAlerts = False
' save under calculated name
ActiveWorkbook.SaveAs [B1] & "-" & Format([B2], "YYYYMMDD-hhmmss")
' turn on alerts again
Application.DisplayAlerts = True
End If
End Sub
and save as a macro enabled template
Then create a [File - New] from this template .... it will immediately be saved under the name of the user with macros removed so that the code can't hit it another time.
The user name could be retrived from the environment or from the registry.
Alternatively you can examine if the file has a true name or (still) is named Book nnn which means it hasn't been saved before; this removes the need to reserve a timestamp cell in your workbook