If one asks whether A and B (objects existing at two different times, or possible worlds, say) are really one and the same object, is this a substantive metaphysical question? I think it is not. Consider the following illustration:
This is how an armless person persists through time. S1 is the momentary stage that exists at t1, and S2 likewise at t2. C is the complete aggregate of all the momentary person-stages from t1 to t2. Now, one might apply the name 'A' at t1, and 'B' at t2, and ask whether A is B. But there are no interesting questions to ask here. It's trivial that S1 is not S2, if that's what we mean. Or, if we instead mean to refer to the temporally extended object C both times, it is similarly trivial that C is identical to itself.
Note that we may similarly construct gerrymandered objects out of completely unrelated temporal parts. For any two distinct stages whatsoever, it is trivial that (1) they are not themselves numerically identical; and (2) we may call them both temporal parts of some larger aggregate. (If you don't like talk of aggregations, we can restate the point in terms of temporal counterparts. Any two stages are counterpart-related by some criterion or other, and our choice of criterion is metaphysically arbitrary.) We merely have practical reasons for carving the world up in some ways rather than others. Gerrymandered objects may be less useful to talk about, but that's not to impugn their ontological status.
Maybe you don't like any kind of 4-dimensionalism or "temporal parts" talk. That's okay, we can restate the point in the language of enduring 3-d objects. We simply need to say that there are arbitrarily many objects coinciding in any given region of space, for all the various possible "persistence criteria" we might want to apply across times. Consider the famous example of a clay statue. Can it survive being turned to gold by Midas' touch? Well, the statue can, but the clay can't. Conversely, the lump of clay can survive being squished into a nondescript blob, but the statue cannot. And we might just as well choose to say there is an object there that "endures" just in case it turns into a bird and flies away. Why not? It's not as though all this persistence talk is reflecting anything deep about the world. We could apply any criteria we want; it's all mere convention.
The alternative view is what Ted Sider (in his (2001) 'Criteria of Personal Identity', p.194) calls "chaste endurantism", i.e. the conjunction of claims (1) objects - no mere temporal parts - are wholly present at multiple moments, and (2) "distinct entities never coincide". But the case of the statue and the clay suggests that this position is a non-starter. There are various criteria we might use to determine whether an object counts as persisting into the future under any given scenario, and no reason to think that any one of these is the only legitimate or "true" criterion.
So I tend to think that the identity facts, such as they are, do not much matter. Indeed, we may completely describe a scenario without talking about the identities of the things in it at all. We would then know all there is to know about how the world (scenario) is; the remaining question is merely how to describe it -- which persistence conditions to apply, or which temporal aggregates to talk about.