Remove shipping name from the label in Cart and Checkout pages https://support.woothemes.com/hc/en-us/community/posts/202866646-Remove-label-for-shipping-method-

remove_shipping_label.php

/**
 * Remove shipping name from the label in Cart and Checkout pages
 */
add_filter( 'woocommerce_cart_shipping_method_full_label', 'wc_custom_shipping_labels', 10, 2 );
function wc_custom_shipping_labels( $label, $method ) {
    if ( $method->cost > 0 ) {
        if ( WC()->cart->tax_display_cart == 'excl' ) {
            $label = wc_price( $method->cost );
            if ( $method->get_shipping_tax() > 0 && WC()->cart->prices_include_tax ) {
                $label .= ' <small>' . WC()->countries->ex_tax_or_vat() . '</small>';
            }
        } else {
            $label = wc_price( $method->cost + $method->get_shipping_tax() );
            if ( $method->get_shipping_tax() > 0 && ! WC()->cart->prices_include_tax ) {
                $label = ' <small>' . WC()->countries->inc_tax_or_vat() . '</small>';
            }
        }
    }

    return $label;
}