The ABN is actually an ATN - an Australian Tax Number!

Well I think so - as the ABN is owned by the ATO and used only for Taxation Purposes!

You still need to register a Business Name separately if you trade under any name other than your own!

Observations on Australian Business Ownership Structures

https://www.business.gov.au/planning/business-structures-and-types

Partnership

This could now be obsolete - with multiple directors now it is easier to simply incorporate a Company and not worth messing around with a Partnership - small partnerships (e.g. husband & wife team) can continue to operate as Sole Traders

Trusts

I personally wouldn't' recommend this for running any sort of serious company that employs people etc ... - more as an instrument to record a company on your financials than anything else ...