Yes, this is a philosophical issue that lies within our attempts to model reality in our systems. What defines identity? A dog named Brian is not the same as a man named Brian.

For value objects, surely Leibniz's philosophy applies: if a theory describes two situations as being distinct, and yet also implies that there is no conceivable way, empirically, to tell them apart, then that theory contains some superfluous and arbitrary elements that ought to be removed.

For entities, it's much more complex.

I still feel some kind of way when seeing classes (with methods!) being used for IDs, though.