Does forming an LLC protect my business name?

Only against another entity registering a confusingly similar name for its formation documents in that same state. It gives you no trademark rights, no protection in other states, and no defence against a trademark owner who used the name before you.

Why did the state approve my name if someone else has the trademark?

Because the state was answering a different question. Business-entity filing offices check their own register of entity names for administrative distinguishability. They do not search the federal trademark register, and approval is not a finding that the name is available to use as a brand.

Is a DBA or fictitious business name any different?

No. A DBA records that a person or entity trades under another name. It is a disclosure mechanism, not a grant of rights, and it confers nothing against a trademark owner.

Do I need to trademark my LLC name?

Not necessarily. You need trademark protection for the name customers use to choose you, which is often not the entity name at all. Many businesses register the brand and leave the holding entity unregistered, which is usually the right way round.

Registering an LLC does not give you a trademark

This is one of the most expensive misunderstandings in small business branding, and it is easy to see how it happens. The state told you the name was available and took your filing fee. The name was available, but only for the narrow thing the state checks.

What the state actually checked

When you form an entity, the filing office compares your proposed name against other entity names on its own register, in that state. The test is administrative distinguishability, so that two companies do not end up indistinguishable on the same list. That is the whole of it.

The filing office does not search the federal trademark register. It does not look at businesses in the other 49 states. It does not ask whether anyone has been selling under that name for a decade. Approval means your paperwork is not confusable with other paperwork in that state. It is not a finding that the name is yours.

What actually creates trademark rights

Two things, and neither is a formation document:

Use in commerce. Selling goods or services under the name creates common-law rights in the geographic area where you actually trade. These are real and enforceable, and also limited to that area.
Federal registration. A registration on the Principal Register gives you a presumption of validity and ownership, and nationwide constructive priority from your filing date, so that later users cannot claim they got there first in a place you had not reached yet.

Neither of those happened when you filed articles of organization.

The sequence that goes wrong

It is remarkably consistent. Form the LLC because the name is available. Buy the domain, also available. Build the site, print the packaging, run ads for two years. Then a letter arrives from a company with a registration that predates everything, and the question becomes what a rebrand costs after you have built equity in the name.

The two checks that were skipped are the cheap ones. State approval and an available domain feel like clearance because both came back green, and neither was looking at trademarks at all. A domain registration in particular is a contract for an address; it tells you only that nobody else has that exact string.

Four registers, four different questions

Part of the confusion is that a founder signs up to several things that all feel like "claiming the name", and each answers a different question.

The entity register at the Secretary of State asks whether another company is filed under a name too close to yours, for administrative purposes, in that one state.
A DBA or fictitious name filing asks whether you have disclosed that you trade under a name other than your legal one. It is a transparency requirement, not a grant of rights.
The domain registry asks whether a string is unclaimed. It applies no legal test at all, and owning a domain has never given anyone trademark rights.
The trademark register asks whether your name, used on your goods, is likely to be confused with someone else's, and whether it is capable of identifying a source at all.

Only the last one is about branding. The first three can all come back clear on a name the fourth would refuse, and none of them looks for the unregistered business already trading under it in another state.

If the LLC is already formed

This is the common position, and it is recoverable. The order to work in:

Search the name properly now, before you print anything or spend on a launch. How to check whether a name is taken covers sound-alikes and unregistered use, which are the parts the state never looked at.
Separate the two names if you need to. Your entity name and your brand do not have to match. Plenty of companies operate as a legal entity with one name and trade under another, which lets you keep the formation you paid for while branding under something clearable.
File for the brand, not the entity. The trademark application covers the name you actually put in front of customers. If those differ, it is the customer-facing one that needs protecting.

The useful reframe

Stop thinking of the entity name as the asset. Customers rarely transact with it. What needs protecting is the name they use to choose you: the product name, the brand on the label, the word they type into a search box. Plenty of businesses run Ridgeline Holdings LLC and register the brand it trades as, which is usually the right way round.

So before the formation filing, or immediately after, run the check the state did not: search the federal register for your brand, including sound-alikes and near-spellings, against goods related to yours. See how to check whether a name is already trademarked, and the three questions that sit behind whether you can use it at all.