Is it possible to hide or encrypt the display name after login into the WordPress admin panel?

If you are talking about the “Howdy” message shown on the admin black bar after login, you can use code similar to this to filter that information.

    add_action('admin_bar_menu', 'lets_change_howdy', 11);

function lets_change_howdy($wp_admin_bar) {
    $user_id      = get_current_user_id();
    $current_user = wp_get_current_user();
    $profile_url  = get_edit_profile_url($user_id);

    if (0 != $user_id) {
        $avatar = get_avatar($user_id, 28);
        $howdy  = sprintf(__('Welcome, %1$s'), $current_user->display_name);
        $class  = empty($avatar) ? '' : 'with-avatar';

        $wp_admin_bar->add_menu(array(
            'id' => 'my-account',
            'parent' => 'top-secondary',
            'title' => $howdy . $avatar,
            'href' => $profile_url,
            'meta' => array(
                'class' => $class,
            ),
        ));
    }
}

This will change the “Howdy (username)” to “Hello (username)”. Adjust as needed for your needs.

It could be that your theme is doing something similar. Search your theme code for that ‘admin_bar_menu’ filter.