The point here is that even though the water is murky about it's intrinsic identity, we know that it's still a particular ship with a particular back story, making at least it's extrinsic identity an immutable known. Fairly similar to how - most, if not all - complex living organisms continually gain and lose composing cells throughout their lives, yet their individual identities remain fixed: "I am X and this is my dog Y".

Similarly, a "fork" as we understand it in the context of software is this thing that, even though it's a modified copy, retains its extrinsic identity: "This software X was worked on in Y context, and is now being worked on in Z+ contexts". Same software, even if it gets a name change.