add-custom-data-in-cart-item-meta.php

<?php
/**
 * Add data to cart item
 */
add_filter( 'woocommerce_add_cart_item_data', 'add_cart_item_data', 25, 2 );

function add_cart_item_data( $cart_item_meta, $product_id ) {

	if ( isset( $_POST ['customer_name'] ) && isset( $_POST ['customer_message'] ) ) {
		$custom_data  = array() ;
		$custom_data [ 'customer_name' ]    = isset( $_POST ['customer_name'] ) ?  sanitize_text_field ( $_POST ['customer_name'] ) : "" ;
		$custom_data [ 'customer_message' ] = isset( $_POST ['customer_message'] ) ? sanitize_text_field ( $_POST ['customer_message'] ): "" ;
		$cart_item_meta ['custom_data']     = $custom_data ;
	}
	
	return $cart_item_meta;
}