List<String> titles = Arrays.asList("First Name", "Last Name");

for (FirstClass first : firstClassList) {
    for (SecondClass second : first.getSecondClassList()) {
        for (ThirdClass third : second.getThirdClassList()) {

            if(!titles.contains(third.getField())) {
                second.getThirdClassList().remove(third);
            }

        }
    }
}