Is there a Field Code that would do it?
No.
You can get the file name using VBA, e.g.
ActiveDocument.MailMerge.DataSource.Name
and also use VBA to insert it in the header of the mail merge main document
/before/ you merge. A fairly easy way to do this would be to assign the
value to a Custome document property and use a DOCPROPERTY field in the
header of the mail merge main document. If you are using Word 2002 or later
you could consider using a MailMerge event to do this.
(NB, if the data source is not a "file" data source (.txt, .doc, .mdb) but
is (say) an ODBC connection to an SQL Server database, then .Name may be
blank)