If you simply business incorporate or register a corporate name, it doesn’t mean that the government approved for you to use the name as a trademark.
If we take a US LLC, as an example, every state has its own laws about business names.
You can register your LLC name in Delaware but the business name registration has no impact on the other 49 states.
In plain English, if you register Coolapples LLC in Delaware, another entity may register Coolapples LLC in Indiana. If you plan to expand nationwide or worldwide, trademark registration will provide that protection. A federal US trademark will give you exclusive rights to use your brand name for your products across the US. Likewise, a Canadian or Australian trademark will give you country-wide rights to use your chosen brand in your country and will make it easier for your to sell or license your trademark later.
To open in a new tab, click: Do I need to register a trademark if my business incorporated?