You sue the business in the name of the LLC. The registered agent is designated to accept service of process in legal matter. Therefore, simply serve the registered agent.
First, you should try to serve the Registered Agent. If the Registered Agent has not maintained their current address with the Secretary of State, you should perform a diligent search to find the Registered Agent. If after a diligent search, you cannot find the Registered Agent, then you may serve the LLC, at its principal place of business, by registered, return receipt requested, mail.
This is for informational purposes only, and you may need to seek the advise of an attorney to assist with your specific situation. No attorney-client privilege has attached because of this response. If you would like to talk about possible representation, please contact my office.