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The twin could be literal: genetic duplicate of the original, hatching from the same shape-shifting, dopplebocking zygote. In that case, there might exist some sibling animosity or maybe a level of fanatical narcissism (depends on how dark you want your plot.)
Or it could be a copycat. Dude copies copier. *insert intellectual property joke*
Or, it could be someone who the doppelganger once copied and now has either developed the shapeshifting ability or can otherwise impersonate the doppelganger. Anyway, they want revenge. Or their some strange Stockholm syndrome fetish thing going on.
Maybe the doppelganger is a patient under treatment in a psyche ward and is confusing one of the orderlies of impersonating them.