Автор: http://www.swissdelphicenter.ch

function ExtractUrlFileName(const AUrl: string): string;
  var
    i: Integer;
  begin
    i := LastDelimiter('/', AUrl);
   Result := Copy(AUrl, i + 1, Length(AUrl) - (i));
  end;

  procedure TForm1.Button1Click(Sender: TObject);
  var
    s: string;
  begin
    s := ExtractUrlFileName('http://www.delphimania.de/index.php');
    ShowMessage(s);  //index.php  
end