Individual Name Fields are not available when adding a new contact
The Editing contact options are listed from option groups named 'Contact Edit Options'. Check if the options are present in the 'Contact Edit Options' option group. If not then adding options should fix the problem. Unfortunately the UI doesn't allow you at add a new option. But you can add it through api/explorer screen of CiviCRM.



Note: Option Name should be the field name same as column name in civicrm_contact table eg first_name, last_name, middle_name etc.