Registering a trademark is not mandatory to make a business website in the United States. If you run a small personal blog or business website and do not have plans to grow it further, then your creative works are already protected by copyright.
On the other hand, if you are doing business across states and plan to grow further, then it becomes essential to register your trademark and copyright.
Registering your trademark and copyright allows you to stop others from using the same or similar business name. You can get exclusive rights to use your trademark for business.
It also makes you responsible for enforcing the trademark. If you find someone infringing your rights, you need to send them a cease and desist letter and take further legal action if necessary.