I mean, the alternate explanation is just that it's a huge coincidence right? That's the story generic Miyu is telling right now at least; a girl with the same name as hers who looks similar to her (though perhaps not the exact same) just happened to move in nearby. Extraordinarily unlikely, but not impossible.And regardless, even if it were that complicated, there's pretty much no other way to explain New Miyu looking identical to and having the exact same name as the original Miyu without resorting to either the supernatural, preternatural, or something similar. “When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth," and all that. If you have some other idea of how this could be, then I would be very interested in hearing about it (or reading about it, I suppose.) Theorizing is what makes mystery stories fun, after all.
Your DID theory is interesting. It's contradicted by the flashbacks we see of the two Miyus both existing in the same physical space, though. You could argue those are actually metaphorical and represent the two alters communicating with each other, but that's still a flaw in your theory.
I do think we'll likely get a big twist at the end, but I don't think it'll be DID. What stands out to me is generic Miyu's continued insistence that real Miyu died because she was "too nice." While she could just mean that she was too nice to see an anonymous person who sent her a letter, it kinda feels like she means more than just that. I think generic Miyu knows more than what she's telling Yuushin. The obvious guess would be that she's the real killer and is looking for someone without an alibi to pin the crime on (we know false allegations are a favorite weapon of hers after all), but that feels a little off to me...