wp_customize changing $args (label, input_attrs, …) in child

For that particular code, you could delete the control and add it back with a different label. Or you could try to set it (must be done after it’s created) like:
$wp_customize->get_control( 'link_color' )->label = 'new label'

Or you could use a plugin like Say What to change text.
https://www.ads-software.com/plugins/say-what/

Thanks Joy. Since I should leave the main theme code unchanged and I do not want this controlled by a plugin I tried the second method in the child functions.php
Found https://developer.www.ads-software.com/reference/classes/wp_customize_manager/get_control/ and https://codex.www.ads-software.com/Class_Reference/WP_Customize_Manager/get_setting
Probably because of chronology of creation (as you noted) it seems to not work:
Warning: Creating default object from empty value in /wp-content/themes/child-theme/functions.php

Yes, the child theme functions run, followed by the parent theme functions. So you need to adjust the priority on the add_action call to make sure the child action runs after the parent’s.

Wow! Thank you again! I was now able to achieve the run after the parent by using (after googling for advise):

add_action( 'customize_register', 'childtheme_customize_register', 20); 
function childtheme_customize_register( $wp_customize ) {
$wp_customize->get_control( 'link_color' )->label = 'new label';
}

So far it seems to run fine…