You'll need to trademark your business name or logo when you'd like exclusive rights to use them and be able to legally prevent others from using it. This is especially within your business area.  See more at IP Australia https://www.ipaustralia.gov.au/trade-marks/understanding-trade-marks. 

Trademarking a business name or logo is generally recommended when you want to protect your brand identity and prevent others from using similar names or logos that could cause confusion among consumers. Here are a few instances when it is important to consider trademarking:

1. Establishing brand recognition: If you want to build a strong brand identity and establish recognition for your business, trademarking your business name or logo can help ensure that others cannot use or imitate your brand.

2. Expanding your business: When you plan to expand your business into new markets or offer new products or services, trademark registration can provide legal protection and help prevent others from using your brand in those markets.

3. Preventing confusion and infringement: Registering a trademark helps protect against potential trademark infringement by other businesses. It allows you to take legal action if someone else uses a similar or identical name or logo that could create confusion among consumers.

The specific timing for trademark registration may vary depending on the jurisdiction and the nature of your business. In some countries, such as the United States, you can establish certain rights to your business name or logo simply by using it in commerce, even without formal registration. However, registering a trademark offers additional legal protection and advantages, such as the ability to bring a federal lawsuit and obtain nationwide protection.

It is generally advisable to consider trademark registration as early as possible, preferably before launching your business or introducing a new brand. This helps ensure that you secure the exclusive rights to your business name or logo and reduces the risk of someone else using a similar mark.

It's important to consult with a qualified intellectual property attorney or trademark professional to understand the specific requirements and processes for trademark registration in your jurisdiction, as laws and regulations may vary.

I’d say as soon as you have a viable product or service that is generating revenue or profit for you. Too often, people get overzealous before testing that they have a profitable business idea. At the start, just registering a business name is enough. Trademarking your business name or logo before you get decent sales or can prove there’s customer demand may turn out to be a waste of your money. But it’s still a good idea to just check the trademark registry to see what has been registered.
 
Once you have a good gauge on the customer demand and proven sales, then it’s worth considering legally protecting your business’s intellectual properties. This can happen just after starting a business, or some time away. However, if your industry is highly competitive or your solution is somewhat unique, it may be advisable to trademark earlier than later, even right from the start.
 
It’s always good to consult an intellectual property or business lawyer. There’s no harm and it’s better to be safe than sorry because you don’t need the headache and financial mess in the event of an IP infringement. 

A person owns a trade mark as they own a computer, car or land. You do not own a Business Name. Business Names are licenced just like car registration plates.  If you want an asset get a Trade Mark.