В /catalog/model/checkout/order.php после (511 строка примерно):

$text .= $language->get('text_new_order_status') . ' ' . $order_status . "\n\n";

вставить

$text .= $language->get('text_new_buyer') . ' ' . $order_info['firstname'] . ' ' . $order_info['lastname'] .  "\n";

$text .= $language->get('text_new_email') . ' ' . $order_info['email'] . "\n";

$text .= $language->get('text_new_telephone') . ' ' . $order_info['telephone'] . "\n";

$text .= $language->get('shipping_city') . ' ' . $order_info['shipping_city'] . "\n";

$text .= $language->get('text_new_payment_address') . ' ' . $order_info['payment_address_1'] .  ' '  . $order_info['payment_address_2'] ."\n\n";

$text .= $language->get('text_new_payment_method') . ' ' . $order_info['payment_method'] . "\n\n";

Проверено на 1.5.5.1.2

Добавится имя, почта, телефон, город, адрес, метод оплаты.