Well, by using the same logic - if they are sworn in using their full legal name and thereafter everyone knows that that is their full legal name because that is how they were sworn in, then why do they need to keep using it?
Part of it boils down to common usage, social convention, and established identity. If my name is John David Andrew Smith, and I've established that sufficiently in the context in which it's being used (let's say court) then the Magistrate doesn't need to keep referring to me as John David Andrew Smith within the court room. I'd be referred to as 'Mr Smith', or perhaps 'Mr John Smith' for certainty. If an order gets made against me, it would use the full name for more certainty when used outside in the broader world.
By the same token, I'm assuming Brad Hazzard was sworn in as Minister (and as MP) using his full legal name - perhaps that is even how you got it. Once done, we know that Bradley Ronald Hazzard is the Minister for Health and Medical Research and that he goes by 'Brad', and that therefore a reference to 'Brad Hazzard' as Minister for Health is surely a reference to 'Bradley Ronald Hazzard', also Minister for Health. Requiring formality adds no benefit (the exception being, though, if there were two Brad Hazzards and you needed to differentiate them in some manner).
Plus, Australian love to abbreviate the hell out of everything. So, requiring otherwise would surely be very un-Australian.