You have forgot to save custom meta field data so check it below code I have done it. Reference
add_filter( 'woocommerce_checkout_fields' , 'occasion_checkout_field_update_order_meta' );
function occasion_checkout_field_update_order_meta( $fields ) {
$fields['billing']['occasion'] = array( 'type' => 'select',
'id' => 'occasion',
'placeholder' => __('Select Occasion', 'woocommerce'),
'required' => false,
'class' => array('form-row-wide'),
'clear' => false,
'options' => array(
'Birthday' => __('Birthday', 'woocommerce'),
'Anniversary' => __('Anniversary', 'woocommerce'),
'Congratulations' => __('Congratulations', 'woocommerce'),
'Sorry' => __('Sorry', 'woocommerce'),
'Good Luck' => __('Good Luck', 'woocommerce'),
'Thank You' => __('Thank You', 'woocommerce'),
'Get Well Soon' => __('Get Well Soon', 'woocommerce'),
'Love' => __('Love', 'woocommerce')
)
);
return $fields;
}
add_action( 'woocommerce_checkout_update_order_meta', 'occasion_checkout_update_order_meta' );
function occasion_checkout_update_order_meta( $order_id ){
if( !empty( $_POST['occasion'] ) )
update_post_meta( $order_id, '_occasion', sanitize_text_field( $_POST['occasion'] ) );
}
add_action( 'woocommerce_admin_order_data_after_billing_address', 'occasion_edit_woocommerce_checkout_page', 10, 1 );
function occasion_edit_woocommerce_checkout_page($order){
echo __('Occasion').': '.get_post_meta($order->id, '_occasion', true );
}