<?php
/* Display the sku below cart item name on Cart BEGIN */
add_filter( 'woocommerce_cart_item_name', 'display_sku_after_item_name', 5, 3 );
function display_sku_after_item_name( $item_name, $cart_item, $cart_item_key ) {
    $product = $cart_item['data']; // The WC_Product Object

    if( is_cart() && $product->get_sku() ) {
        $item_name .= '<br><span class="item-sku">'. $product->get_sku() . '</span>';
    }
    return $item_name;
}
/* Display the sku below cart item name on Cart END */

/* Display the sku below under cart item name in checkout BEGIN */
add_filter( 'woocommerce_checkout_cart_item_quantity', 'display_sku_after_item_qty', 5, 3 );  
function display_sku_after_item_qty( $item_quantity, $cart_item, $cart_item_key ) {
    $product = $cart_item['data']; // The WC_Product Object
    if( $product->get_sku() ) {
        $item_quantity .= '<br>SKU: <span class="item-sku">'. $product->get_sku() . '</span>';
    }
    return $item_quantity;
}
/* Display the sku below under cart item name in checkout END */