Display the sku below cart item name in WooCommerce. There are 2 functions below. One is for the Cart page and the other is for the Checkout page.

/* 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 */