Consider an unique object id. It need not be expensive to calculate and it doesn't matter in the slightest how often it will be used. It might not be used by the object itself. But it must be immutable once defined.
For instance: a "dogs" class; the unique id is a sequential integer. When I instantiate Scruffy, nobody else knows or cares how many dog objects I have created in the past, so the value must come from the class itself. The pet_store class will need the id to complete the sale, the obedience_school class wants to know who will be showing up, the vet class needs to keep track of rabies shots, and the pet_cemetery class will want to know who's in crypt #53. Or, none of these if I'm the breeder, own a chain disreputable restaurants and just need to keep track of tonight's special.