WordPress – Custom Nav menu for logged in users – Shopkeeper theme

I think you already did part of this but i am detailing all steps:

1.- Register 2 nav menus:

register_nav_menus(array(
            'logged-in' => __('Logged In Menu', 'yourthemename'),
            'logged-out' => __('Logged Out Menu', 'yourthemename')
        ));

2.- Create the menus going to Appearence -> Menus in the back-end, assign each one to his corresponding location.
3.- Where you have the Menu displaying (i guess is in header.php) put this:

$theme_location = 'logged-out';//default value

if( is_user_logged_in() ) {
    $theme_location = 'logged-in';//user is logged in change the menu name
}
wp_nav_menu(array(
        'theme_location' => $theme_location,
        'menu_class' => 'my-menu',
));