ASX use a system called CHESS (Clearing House Electronic Subregister System) to track ownership and facilitate settlement of securities traded on the ASX.
When you create an account with a broker, you are allocated a 'Holder Identification Number' or 'HIN'. This number identifies you as a CHESS-sponsored shareholder. You should keep your HIN private in the same way as you would a bank account number, as it can be used to personally identify you and access your holdings.
With SelfWealth, each trading account is allocated one HIN. As such you can have multiple holdings under a single HIN, and even have multiple HINs under one name. You can identify a HIN as it will begin with the letter 'X' followed by 10 numbers (e.g. X0001234567).