Woocommerce Removing "Additional information" Name On Checkout Page

try to add this to your functions.php

add_filter('woocommerce_enable_order_notes_field', '__return_false');

To remove the whole Additional information section use:-

add_filter('woocommerce_enable_order_notes_field', '__return_false');

And If you just want to remove the Additional information text:-

function wc_order_review_strings( $translated_text, $text, $domain ) {  if(is_checkout()){    switch ($translated_text) {      case 'Billing details' :        $translated_text = __( 'Billing Info', 'woocommerce' );        break;      case 'Additional information':        $translated_text = __('New Field Name', 'woocommerce');        break;     case 'Your order':        $translated_text = __('My Order', 'woocommerce');        break;     case 'Product':        $translated_text = __('Your Product', 'woocommerce');        break;    }  }  return $translated_text;}add_filter( 'gettext', 'wc_order_review_strings', 20, 3 );

The Additional Information title is located in file:

wp-content/plugins/woocommerce/templates/checkout/form-shipping.php

However i recommend you to create a child theme and make your customizations there. Adding the filter that @qutek recommends also works.

If you want to get rid of the 2 columns style that the checkout comes with, you should customize the div with the "customer_details" id located in file:

wp-content/plugins/woocommerce/templates/checkout/form-checkout.php