Probably the easiest way is to manually construct a new Billing address format by creating a copy of the WooCommerce email address template in /your-theme-driectory/woocommerce/emails/email-addresses.php by replacing the original echo $order->get_formatted_billing_address(); with for example:
$output="<strong>Customer Name: </strong>".get_post_meta($order->id, '_billing_first_name', true).'<br>';
$output .= '<strong>Customer Last Name: </strong>'.get_post_meta($order->id, '_billing_last_name', true).'<br>';
$output .= '<strong>Company Name: </strong>'.get_post_meta($order->id, '_billing_company', true).'<br>';
$output .= '<strong>Country: </strong>'.WC()->countries->countries[get_post_meta($order->id, '_billing_country', true)].'<br>';
echo $output;