My question involves labor and employment law for the state of: Any state

When a background check is done and when a name is asked to be put down does it need to be exactly as that mentioned in the social security (with middle name) or can it only have first and last name only. I am the plaintiff in a civil lawsuit that includes foreign defendants which include national agencies, my landlord and my employer. The lawsuit was dismissed for want of jurisdiction due to sovereignty of the foreign national agencies. Future employers may find the case in which case what are the consequences I may face for such public exposure? Currently trying to suppress the sites.