If you are using Word XP or later, I have created an add-in that will do
that.  You can find it on fellow MVP, Graham Mayor's website at:

http://www.gmayor.com/individual_merge_letters.htm

If you have Word 97, here's the method that I used to use 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