In mutating models, typically abstract (mathematical / conceptual) objects are modeled as memory locations. Which means that object identity implies pointer identity. But that's a problem when different versions of the same object need to be maintained.
It's much easier when we represent object identity by something other than pointer identity, such as (string) names or 32-bit integer keys. Such representation allows us to materialize us different versions (or even the same version) of an object in multiple places, at the same time. This allows us to concurrently read or write different versions of the same abstract object. It's also an enabler for serialization/deserialization. Not requiring an object to be materialized in one particular place allows saving objects to disk or sending them around.