The following macro will do it:

Sub splitter()

' splitter Macro

' Macro created by Doug Robbins to save each letter created by a mailmerge
as a separate file.

Dim i As Long, Source as Document, Target as Document, Letter as Range
Set Source = ActiveDocument
For i = 1 to Source.Sections.Count
   Set Letter = Source.Sections(i).Range
   Letter.End=Letter.End-1
   Set Target = Documents.Add
   Target.Range=Letter
   Target.SaveAs FileName:="Letter" & i
   Target.Close
Next i

End Sub

Here's another method that I have used that involves creating a separate
catalog type mailmerge maindocument which creates a word document containing
a table in each row of which would be your data from the database that you
want to use as the filename.

You first execute that mailmerge, then save that file and close it.  Then
execute the mailmerge that you want to create the separate files from and
with the
result of that on the screen, run a macro containing the following code
and when the File open dialog appears, select the file containing the table
created by the first mailmerge

' Throw Away Macro created by Doug Robbins
'
Dim Source As Document, oblist As Document, DocName As Range, DocumentName
As String
Dim i As Long, doctext As Range, target As Document
Set Source = ActiveDocument
With Dialogs(wdDialogFileOpen)
   .Show
End With
Set oblist = ActiveDocument
Counter = 1
For i = 1 To oblist.Tables(1).Rows.Count
   Set DocName = oblist.Tables(1).Cell(i, 1).Range
   DocName.End = DocName.End - 1

   'Change the path in the following command to suit where you want to save
the documents.
   DocumentName = "I:\WorkArea\Documentum\" & DocName.Text
   Set doctext = Source.Sections(i).Range
   doctext.End = doctext.End - 1
   Set target = Documents.Add
   target.Range.FormattedText = doctext
   target.SaveAs FileName:=DocumentName
   target.Close
Next i