LLC

I'm not clear what you mean when you discuss adding your name. I'm assuming that you're talking about becoming a member of the LLC (LLCs have members, whereas corporations have shareholders). It could also mean that you might become a non-member manager. As to whether its appropriate for you to assume ownership in, or management of, the LLC is dependent upon a number of business decisions. With the limited information you've provided, no one can tell you whether it would be recommended or appropriate to "add your name" to the company. As far as how to do it, membership interests are recorded in the official books and records of the company, they are not recorded by the Secretary of State's office. To get advice tailored to your situation, you may wish to consult a lawyer.

This answer is for informational purposes only, and cannot be relied upon as legal advice. For advice tailored to your situation, consult an attorney licensed in your state.

It is not clear whether your husband created an LLC in his name, e.g., John Doe, LLC, and you now want to change the name to John Doe and Jane Doe, LLC, or whether your husband created an LLC that he owns named XYZ, LLC, and now he wants you to share the ownership of the LLC. If it is a name change, it will involve recording appropriate documents with the Secretary of State or similar state office. If it is a matter of making you a co-owner, he will assign a membership interest in the LLC to you.

You may be able to get enough information from the Secretary of State or other state office dealing with LLC's or you may need counsel to implement the changes.