My boyfriend did the citizenship hoopla last year for HECS. The exam is only part of the process, which is to say makes you eligible to go to the citizenship ceremony. You're not a full citizen at this point. You are not officially deemed a citizen until you attend the ceremony, say the pledge (you seriously have to do this or you don't get the certificate) and receive the certificate - they are VERY anal about this, and I think you can only forego the ceremony under exceptional circumstances. You also can't just ask for a ceremony to be done just for you. They'll try and slot you in to your local council (as they're the ones that run the ceremonies) and some do it only once or twice a year :/ Some council chambers, like Kogarah council, only allow council residents to take part in the citizenship ceremony there. So make sure that if you do find a ceremony that you can actually attend it. If the ceremony is a few weeks after census date, you're out of luck, it won't count
When you get your citizenship ceremony all done you should contact UNSW and get them to change it, and probably best to do that in person. You've got until the end of March, so hopefully you can slot into a ceremony somewhere.