Perhaps you should further explain your situation as I don't think I understand it fully...

The last time that I checked, the positions of items in ArrayLists don't change unless you change them manually. I don't see why you would want to do this for any practical reason and, even if you did, to sort them, for instance, the change would only occur when you add new values.

If you are still unable to keep track of items in the ArrayList, you can create an ID system in which each item has an ID variable that is defined at initiation. You can then set up a function to iterate through the ArrayList and return the item with the specified ID, although this can cost time (not that much, and not a worry if framerate isn't all that important for your implementation) and can be confusing and should thus be avoided unless you are certain that you need it.

It would be clearer if you described a concrete case (what is your need, exactly?) as your example isn't clear (and naming a class "Object" is prone to be troublesome!).

Ah, perhaps what you look for is a HashMap!

1. class Foo {
2.   int number = 5;
3.   void action() {
4.     println("I do an action; number = " + number);
5.   }
6. }
7.  
8. void setup()
9. {
10. HashMap<String, Foo> foo = new HashMap<String, Foo>();
11.  
12. //sue, joe, bob, steve, and sirRodricTheThird.
13. foo.put("Sue", new Foo());
14. foo.put("Joe", new Foo());
15. foo.put("Bob", new Foo());
16. foo.put("Steve", new Foo());
17. foo.put("sirRodricTheThird", new Foo());
18. Foo identify;
19. identify = foo.get("Sue");
20. identify.action();
21. identify = foo.get("sirRodricTheThird");
22. identify.number = 45;
23. identify.action();
24. exit();
25. }

Doesn't java have a hashcode() function to get a specific identifier? Oh yes it has .... just checked on google. You can use the hashcode output as an identifier. It is a good idea to put the objects into a directory of some sort, probably as a hashmap. But!!! can i  suggest that what you're really thinking of is a global environment context, through which the object can operate in and interact with other object? 

Avoid using the hashcode as an identifier it is more complex to use than suggested. PhiLho's suggestion of using the HashMap is spot on but the example below is probably closer to the sort of thing you need.

1. HashMap<Integer, Foo> foos;
2. Foo foo;
3. 
   
4. public void setup() {
5.   foos = new HashMap<Integer, Foo>();
6.   createFoos();
7.   displayFooName(299);
8.   displayFooName(666);
9.   displayFooName(111);
10.   displayFooName(202);
11. }
12. 
    
13. public void displayFooName(int fooID) {
14.   foo = foos.get(fooID);
15.   if (foo != null)
16.     println(foo.name);
17.   else
18.     println("Can't find foo " + fooID);
19. }
20. 
    
21. public void createFoos() {
22.   foo = new Foo(701, "Pandora");
23.   foos.put(foo.id, foo);
24.   foo = new Foo(202, "PhiLho");
25.   foos.put(foo.id, foo);
26.   foo = new Foo(299, "Quarks");
27.   foos.put(foo.id, foo);
28.   foo = new Foo(888, "Lucky");
29.   foos.put(foo.id, foo);
30.   foo = new Foo(666, "Lucifer");
31.   foos.put(foo.id, foo);
32. }
33. 
    
34. public class Foo {
35.   int id;
36.   String name;
37. 
    
38.   public Foo(int pid, String pname) {
39.     id = pid;
40.     name = pname;
41.   }
42. }