It's generally thought that an object must have at least one criterion of identity. It's also said that a criterion of identity must come along with a principle of unity. An object must also have some kind of temporal longevity if it is to be deemed an object in the first place.
How can an object have temporal longevity?
It does so because it has a principle of unity. That principle tells us that certain properties of the object unify it and they do so because they also tell us what aspects of the object must remain in order for that object to remain as that very same object over time. The unity of the object is what makes it the thing it is over time.
It was traditionally thought that the object’s essence determined what we class as a criterion of identity. However, just as we had choices as to what could be criteria of identity, so we have choices as to what constitutes the essence of a single object. One set of essential properties may work for one group of individuals or one set of situations, and another set may work for another group of individuals or set of situations. Why assume that there's the real essence of an object and no more? Perhaps it depends on the ‘modes of presentation’ of that object. And each different mode of presentation will determine its own essence. Under the mode of presentation that is physics, an object may have an essence specified in terms of its molecular and atomic structure. This would be a constitutional or inherent essence. Under the mode of presentation of, say, people who relate to - or use - the object under scrutiny, the essence may be specified in terms of that object’s role/purpose or its relation to the scrutiniser/s.
Many people will have different ways of individuating the very same object. It may depend on how that object is seen - both literally and metaphorically. It may depend on our particular relation or lack thereof to that object. It may also depend on the cognitive baggage that we bring to the object under scrutiny. People with different beliefs and different sets of knowledge will individuate the very same object in different ways. We could have a God’s-eye view of the object; though wouldn’t that view involve an infinite conjunction of the properties and the relations that belong to the object? Alternatively, perhaps a God’s-eye view of the object would entail an infinite disjunction instead. An infinite set of possible characterisations or individuations of the object. In that case, mortal individuators couldn't use infinite conjunctions or disjunctions. Mere mortals couldn't even comprehend them. A God’s eye view of the object at hand would only be of use to the person with God’s eye – viz., God himself.