Get chosen shipping method title by its Id in WooCommerce

$rate_table = array();

$shipping_methods = WC()->shipping->get_shipping_methods();

foreach($shipping_methods as $shipping_method){
    $shipping_method->init();

    foreach($shipping_method->rates as $key=>$val)
        $rate_table[$key] = $val->label;
}

echo $rate_table[WC()->session->get( 'chosen_shipping_methods' )[0]]; 

Try like this

If the customer has calculated the shipping on the front end, this should work:

function get_shipping_name_by_id( $shipping_id ) {
    $packages = WC()->shipping->get_packages();

    foreach ( $packages as $i => $package ) {
        if ( isset( $package['rates'] ) && isset( $package['rates'][ $shipping_id ] ) ) {
            $rate = $package['rates'][ $shipping_id ];
            /* @var $rate WC_Shipping_Rate */
            return $rate->get_label();
        }
    }

    return '';
}

This will return an empty string if it couldn't find a name for the given shipping id.