You are under no obligation to register your trade mark or brand name. 

However, if you do not register your trading name, you should be aware of the following:

If a third party copies your brand name the only action you can take against that third party is to commence proceedings for ‘passing off’ (i.e. because a third party is ‘passing off’ their goods / services as yours) in order to prevent the unauthorised  use of your brand name. 

However, establishing a claim for passing off can be difficult.

Owning a registered right over your brand name is the most effective way of preventing third parties from using your mark without your permission. 

If you choose NOT to apply for a registered trade mark, there is also the risk that a third party will register a mark that is confusingly similar or identical to your mark and subsequently accuse you of trade mark infringement and prevent you from using your mark.