How can I change a function in a parent theme via a child themes functions.php

On the init action, remove the action calling their function and enqueue an action calling your (differently named) function, like this:

add_action('init', 'wpse_80107_init');

function wpse_80107_init() {
    // remove parent theme's header content action
    remove_action('cyberchimps_header_content', 'cyberchimps_logo_icons');

    // add child theme's header content action
    add_action('cyberchimps_header_content', 'wpse_80107_logo_icons');

}

function wpse_80107_logo_icons() {
    // your custom code here
}