Define your business

Before filing anything, decide what you sell, where you’ll operate and what you’ll call the business.

Do this

Write one sentence. What you sell, to whom, and where. “Mobile dog grooming for households in one county” is enough. Forms, license lookups and lenders all ask for it.
Decide where you’ll operate. Your location decides your taxes, zoning and rules. Zoning applies to home-based businesses too.
List three possible names. A short list beats one favorite, because the checks below may cross some off.
Check each name against your state’s records. Your state’s Register your business page links to the database and says what the state checks.
Check the federal trademark database at the USPTO. A trademark can block a name in your line of work in every state.
Check the domain. Something close to the name is fine.
Decide whose name goes on the door. Using a business name instead of your own may mean registering a DBA, which your state’s registration step covers.

What you get back

A one-line description, an address, and a name that passed both searches. Neither search catches every name already in use. Nothing is filed yet, and nothing here costs money.

When to get help

If your name is close to an existing trademark, a trademark attorney can tell you how close is too close. For the idea itself, the SBA’s partners offer free or low-cost counseling.

Where your state differs

Arizona: The Corporation Commission checks a new LLC or corporation name against corporations, LLCs and registered trade names. It doesn't check trademarks or names people use without registering, so search the web too. Source
California: The Secretary of State checks a new LLC or corporation name only against entities of the same type. It doesn't check county business names or trademarks, so an approved name can still collide with someone else's. Source

Common questions

How do I check if a business name is taken?

Search your state's business records and the USPTO's federal trademark database. A name can be free in one and taken in the other.

Do I need to trademark my business name?

You don't have to. A trademark protects a name nationally within your line of work. If you want one, the SBA suggests filing with the USPTO once your business is formed.

Does my website domain have to match my business name?

No. If the exact name is taken, a close variation works.

What is a DBA?

A DBA ("doing business as") lets you operate under a name other than your own or your registered entity's. It doesn't protect the name, and some places require it.