Change wc_cart_totals_shipping_method_label function in Woocommerce
As you can see in this function you can use woocommerce_cart_shipping_method_full_label filter hook, to manage that change, this way:
add_filter( 'woocommerce_cart_shipping_method_full_label', 'change_cart_shipping_method_full_label', 10, 2 );function change_cart_shipping_method_full_label( $label, $method ) { $has_cost = 0 < $method->cost; $hide_cost = ! $has_cost && in_array( $method->get_method_id(), array( 'free_shipping', 'local_pickup' ), true ); if ( ! $has_cost && ! $hide_cost ) { $label = $method->get_label() . ': Free'; } return $label;}Code goes in function.php file of your active child theme (or active theme). Tested and works.