public static void removeTheFirstNameDuplicates(Map<String, String> map) {
    //напишите тут ваш код
    Iterator<Map.Entry<String,String>> i = map.entrySet().iterator();
    String pastName = "";
    while (i.hasNext()) {
        String curName = i.next().getValue();
        if (!curName.equals(pastName)) {
            pastName = curName;
        }else {
            removeItemFromMapByValue(map, curName);
        }
    }

}

public static void removeItemFromMapByValue(Map<String, String> map, String value) {
    Map<String, String> copy = new HashMap<>(map);
    for (Map.Entry<String, String> pair : copy.entrySet()) {
        if (pair.getValue().equals(value)) {
            map.remove(pair.getKey());
        }
    }
}

public static void main(String[] args) {
    Map a = createMap();
    System.out.println(a);
    removeTheFirstNameDuplicates(a);
    System.out.println(a);
}