import java.util.*;
import java.io.*;


public class FileCreator{

    public static void main(String[] args) throws Exception{

        File f = f = new File(".");
        File[] files = f.listFiles();

        for(File fl : files){
            String fileName = fl.getName();
            if(fileName.contains("Copia - Copia")){
                    System.out.println(fileName);
            }

        }
    }
}

Pattern p = Pattern.compile("");
    Matcher m;

    f = new File(".");
    File[] files = f.listFiles();

    for(File fl : files){
        String fileName = fl.getName();
        m = p.matcher(fileName);
        if(m.find()){
            //fl.delete();
            System.out.println(fileName + " deletado");
        }
    }

Copia - Copia\.[^.]+$
^                ^   ^
1                2   3

import java.util.ArrayList;
import java.util.List;
import java.util.regex.Pattern;
import java.util.regex.Matcher;

class Exemplo
{
    public static void main(String[] args)
    {
        final Pattern regex = Pattern.compile("Copia - Copia\.[^.]+$");

        List<String> files = new ArrayList<String>();

        files.add("File 123 - Copia.txt");
        files.add("File 10 - Copia - Copia.java");
        files.add("File 12 - Copia.java");
        files.add("File 14 - Copia - Copia.txt");
        files.add("File 16 - Copia.txt");
        files.add("File 18 - Copia - Copia.log");
        files.add("File 2 - Copia.txt");
        files.add("File 4 - Copia.log");
        files.add("File 6 - Copia - Copia.txt");
        files.add("File 8 - Copia.txt");

        for (String file : files)
        {
            if (regex.matcher(file).find())
            {
                System.out.println("Encontrado: " + file);
            }
        }
    }
}

.*Copia - Copia\.[^.]+$
^  ^               ^   ^
1  2               3   4

for (String file : files)
{
    if (file.matches("Copia - Copia\.[^.]+$"))
    {
        System.out.println("Encontrado: " + file);
    }
}

Pattern.compile("Copia - Copia\.[a-zA-Z]{3,4}$");

String trechoParaRemover = "(Copia - Copia)";
fileName = filename.replace(trechoParaRemover,"");