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You because you registered and formed the LLC first.
To register the business
name - that means that no other business with exactly the same name
has an active (up to date) registration on the state's database.
However, there may be businesses of record with that name that are no longer active. There may be businesses in other
states or countries that do business under that name. There may even be businesses in the same state that are operating under that name, but have not yet registered - only you can use the name once registered in that state.
So, you can send them a cease and desist letter. If they continue using that name without your consent then you will have no alternative but to file suit.