What document do I use to legally remove my name from an LLC and its liabilities?
When you say "remove my name" from a limited liability company, I assume that you mean that you are a member of the LLC and want to resign. This called "withdrawal" from the LLC.
The addition or resignation of member of a limited liability company is governed by your LLC's operating agreement.
All limited liability formations performed at LegalZoom include a customized operating agreement, which includes provisions and forms for the removal/withdraw of members as well as dissolving the LLC.
Some LLC operating agreements permit withdrawals only if the other members agree. Other operating agreements let a member withdraw for any reason. It entirely depends on what the members agreed to.
In the absence of an operating agreement--or if the operating agreement is silent on the issue of withdrawal--then your state's LLC statute will govern. Most state LLC statutes describe under what circumstances a member may withdraw from an LLC, how much notice they must give the other members, and so forth.
Therefore, with a limited liability company already in existence, you will have to review your operating agreement.
Some states require that a form be filed with the state when membership in an LLC changes. Any of the advertisers on this site can help you with that process for a reasonable fee.
This is distinguished from a "dissolution" which terminates the LLC's existence.
Dissolving a limited liability company requires filing a form--called Articles of Dissolution-with your state. Legalzoom has Articles of Dissolution for each state, and will dissolve your LLC for you starting at $129+ state fees (pricing as of August, 2008).