If you set up your business as just a sole trader, then your information is going to be available online. That means your full name, and the postcode of ABN registration.
If you incorporate an Australian company - let's call it John Smith Pty Ltd - there isn't going to be much online that I can find for free. I'll be able to see the company's name, its ABN / ACN, and its postcode of registration. If I wanted to look up who is a director or shareholder of John Smith Pty Ltd, I have to pay for the information from ASIC first. Yes, it's︀ not that expensive, but it's a pain in the a*s and nobody is actually going︁ to do it.
If you were to incorporate a US LLC with John Smith Pty︂ Ltd being the sole member and manager, you could do business through the US LLC︃ and send your profits to the Australian company and your Aussie company would pay tax︄ on that income because most US LLCs are "pass-through" tax entities, meaning the income gets︅ passed straight through to members.
If you incorporate an Australian company - let's call it John Smith Pty Ltd - there isn't going to be much online that I can find for free. I'll be able to see the company's name, its ABN / ACN, and its postcode of registration. If I wanted to look up who is a director or shareholder of John Smith Pty Ltd, I have to pay for the information from ASIC first. Yes, it's︀ not that expensive, but it's a pain in the a*s and nobody is actually going︁ to do it.
If you were to incorporate a US LLC with John Smith Pty︂ Ltd being the sole member and manager, you could do business through the US LLC︃ and send your profits to the Australian company and your Aussie company would pay tax︄ on that income because most US LLCs are "pass-through" tax entities, meaning the income gets︅ passed straight through to members.