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