Explanation for what exactly? To have your civil acts written in book kept by government - it's definitely not soviet invention, before USSR it was kept by church at least since 18th century.
You pay few thousands to regional officer in any district and they issue you a handwritten internal id book [0] with whatever name you want and there is no trace of it. If something happens they would claim that id form was fraudulent or stolen.
However, when you get tax number, it goes through central office and leaves paper trail and entry in some database that records such issuance.
[0] http://images.delcampe.com/img_large/auction/000/226/943/305...