I don't think there is a noun for the verb "to press charges", hence my above suggestion.

Another alternative would be "claimant" the person who claims the wrong-doing of another person.

Out of
Dietl, Dict. of Legal Terms
Romain, Dict. of Legal Terms

Usually, an Anzeigereerstatter is a person who has filed a complaint with the police. Such a complaint relates to a criminal act on the part of the person being charged. In such case, the Anzeigenerstatter can be called the complaining party orcompainant. In the States at least we would not usually call this person an informant.An informant usually stays out of the picture. He tells the police but doesn\'t want his name known.
If this is a civil case, however, then the party filing the suit is called a Plaintiff in most courts, but sometimes Complainant. We do not usually see such person being called an Anzeigenerstatter,\" but I don\'t rule it out.
Let your context be your guide.
A retired, old lawyer.

the person who files a complaint