The person may be called a persuader, influencer or at best a counsellor as the case or situation may be. The person may render his service free or against service charges mutually settled.
the person who files against you. the complainant
the plaintiff, that is the person filing the complaint against you.
If you refering to what is the term for a person who is trying the state's case against the defendant, they are called the Prosecutor.Added: His opposite number in the courtroom, would be the Defense Attorney.
At the trial court level, the parties are called "plaintiff" for the person making the claim, and "defendant" for the person defending against it. In a criminal case, the person making the claim is the "prosecutor" or the district attorney in some situations, and the accused is called the "defendant." At the appeals level after the trial, the sides are called "appellant", for the person making the appeal from the trial court decision, and "respondent" for the person responding to the appeal.