Business formation is done under state law. Thus, if your business is registered with the state as an LLC, you have a LLC. If the feds have a typo on one or more your tax forms, talk to your accountant about making the correction.
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No, you simply need to notify the IRS of its typographical error. Send the IRS a copy of the Secretary of State's certificate and that should do the trick; include a copy of the IRS paperwork so they know to match them up.
i agree with my colleagues.
I would only add that you want to make sure the IRS has your tax ID number registered under the appropriate tax status. If you want to be taxed as a sole proprietorship, then your tax status for the LLC should be "disregarded entity." If you are registered as a partnership, then the IRS will be looking for a partnership return for your EIN while you will simply be filing your personal Form 1040.
LLCs are unique in that they get to choose how to be taxed. Depending on how many members there are, an LLC can be a "disregarded entity," a partnership or a corporation for tax purposes. You just want to make sure that you and the IRS have the same idea about your LLC.