Your LLC was formed under state law and the name was registered when organized. You need to have the named changed at the state level first.
Then you can change the name at the federal level based on your facts.
See the attached IRS link noted in @Carl response.
If you are sending in a letter, then I recommend you send it certified mail return receipt requested.
*A reminder that posts in a forum such as this do not constitute tax advice.
Also keep in mind the date of replies, as tax law changes.
