How to find out who owns a business in Australia
The ABN record shows the entity behind a business: for a sole trader that's the person's name; for a company, the company name and ACN; for a trust, the trustee arrangement's name.
Companies
The ABN register doesn't list directors or shareholders. For a company, those are held by ASIC and can be obtained through an ASIC company extract (fees apply).
Business names
A business name is registered to an entity with an ABN. Search the business name here, open the result and you'll see the legal entity that holds it.