Altering term_id and name via $wpdb class

You can do it easily. Your query should be:

$querystr = "SELECT `term_id` AS `id`, `name` AS `value`, `slug`, `term_group` FROM {$wpdb->terms} WHERE lower($wpdb->terms.name) like '%$s%'";

See, here i’ve mentioned the name of the fields needed. For any other fields, you need to explicitly mention the field names.