If you follow the recent judgement of Kunc J in Leslie George Lobsey v Liverpool Plains Shire Council  NSWSC 446, the answer to this question may well be: not a lot.
The situation in this matter is rather unusual. Among other things, in this matter Mr Lesley George Lobsey sought relief from the Liverpool Plains Shire Council (“the Council”) because employees of the Council addressed letters to him using his given name. Mr Lobsey asserted that by sending these letters the Council and its employees breached the “common law” copyright, and the common law “trademark” and “tradename” that Mr Lobsey holds in his own name. Consistent with this position, Mr Lobsey signed his Statement of Claim as “L Lobsey ‘TM’”.
In this decision, Kunc J labelled the allegations made in Mr Lobsey’s Statement of Claim as “plainly hopeless”. The following paragraphs (18-20) from the decision illustrate why:
“Insofar as Mr Lobsey claims something in the nature of “common law copyright”, that claim is unsustainable because copyright is exclusively a creature of statute in the form of the Copyright Act 1968 (Cth). Even if Mr Lobsey were to rely on that legislation, there is no doubt that Mr Lobsey’s name is not a “literary work” within the meaning of that Act and is not capable of receiving any copyright protection. Even if it were, I can see no basis upon which Mr Lobsey could claim to be the “author” of his own name. If anyone was the author of his name, it would be his parents.
Insofar as Mr Lobsey’s claim is based on a “common law trademark or tradename”, there is again no such thing. Such matters are governed by the Trade Marks Act 1995 (Cth). Reliance on that legislation would fail at the first hurdle, given that his name is not a name used by him or intended to be used by him to distinguish goods or services dealt with or provided in the course of trade by a person from goods or services so dealt with or provided by any other person as defined in s 7 of that Act. Furthermore, on the basis of evidence provided by the first to third defendants, Mr Lobsey has never registered his name as a trademark nor has he ever applied to do so.
The only relief to protect something in the nature of a trademark or tradename available at common law would be a claim for passing off. However, on no view could it be said that sending a letter to Mr Lobsey at his home using his given name could constitute passing off by any of the defendants.”
The Council made an offer to Mr Lobsey to end the proceedings before the matter went to Court, but this offer was rejected by Mr Lobsey. Kunc J held that this rejection was unreasonable because “properly advised, Mr Lobsey should have understood that his claim was hopeless” and consequently Mr Lobsey was ordered to pay the defendants’ costs.