WordPress cronjob get scheduled but function does not run

I believe you need to use wp_get_current_user() (see https://codex.wordpress.org/Function_Reference/wp_get_current_user ), which will return the current WP user information as an object.

From there, you can get the user name (or other parameters). From that page, this example should get you started:

$current_user = wp_get_current_user();
    /**
     * @example Safe usage: $current_user = wp_get_current_user();
     * if ( !($current_user instanceof WP_User) )
     *     return;
     */
    echo 'Username: ' . $current_user->user_login . '<br />';
    echo 'User email: ' . $current_user->user_email . '<br />';
    echo 'User first name: ' . $current_user->user_firstname . '<br />';
    echo 'User last name: ' . $current_user->user_lastname . '<br />';
    echo 'User display name: ' . $current_user->display_name . '<br />';
    echo 'User ID: ' . $current_user->ID . '<br />';

The get_current_user() function you used is a PHP command, not a WP command. It will return the user that is running the script. See http://php.net/manual/en/function.get-current-user.php