Child them function.php ‘parent-style’: should I name this as parent theme name?

You can leave it as is (see Jacob Pettie’s comment) or you can change it, but the key here is to add the path to locate the parent theme’s CSS.

<?php
add_action( 'wp_enqueue_scripts', 'my_theme_enqueue_styles' );
function my_theme_enqueue_styles() {
    wp_enqueue_style( 'parent-style', get_template_directory_uri() . '/style.css' );
 
}

In your example you’re cutting it off after the ( ‘parent-style’ ), but you should continue and include the path to the parent theme’s style.css.

get_template_directory_uri() is for the parent theme.

The full step by step breakdown can be found here: https://developer.wordpress.org/themes/advanced-topics/child-themes/