Direct answer
An LLC creates a state-level business entity. A trademark protects a brand identifier used with goods or services. Forming an LLC does not automatically give you federal trademark protection, and registering a trademark does not create a business entity.
What an LLC does
An LLC establishes a legal business entity under state law. It can help separate business obligations from the owner personally, subject to applicable law and how the company is operated. The state entity name is not the same thing as a federal trademark registration.
What a trademark does
A trademark identifies the source of goods or services. Federal registration can provide important nationwide benefits, but the USPTO examines whether the mark is eligible and whether conflicting rights may exist.
Which should come first
There is no single sequence for every business. If the LLC will own the trademark, forming the entity first may simplify ownership. If a brand name is commercially critical, searching the name before investing heavily in formation, packaging or marketing can reduce rebranding risk.
Why business-name availability is not enough
A state may allow an LLC name even when a similar federal trademark exists. State entity databases and the federal trademark register answer different questions, so checking one does not replace checking the other.