Right, remember the 50th anniversary special, the Day of the Doctor? The one with Matt Smith, David Tennant and John Hurt in it? Among the myriad goings-on in that episode was an invasion by the shapeshifting Zygons…through 3D paintings because Gallifrey Daleks Peter Capaldi eyebrows. Or something.
Anyway, at one point a Zygon starts imitating Osgood and is really mean to her. Then later in the episode, in order to broker a peace deal, the Doctor wipes everyone’s memory so humans and Zygons can’t remember if they’re humans or simply Zygons pretending to be humans.
Perhaps the Zygon’s memory never came back, and she has been living as Osgood since then. Perhaps, with the original human Osgood dead, Ozgood is only now recalling her origins, a kind of sleeper cell. Perhaps, perhaps, perhaps.
As with the survival of Missy, ‘vaporisation’ special effects are nice and vague and are often revealed to be a disguised teleportation. You only have to think back to the episode Time Heist for an example: those suicide pills actually transported the Doctor’s gang to safety.
It is possible that Missy’s strange smartphone/weapon is a modern update of the Master’s old Tissue Compression Eliminator. This used to shrink victims down to doll-size through “matter condensation.” An improved version would presumably mean better shrinkage. Could a tiny, subatomic Osgood still be alive and well, living in Missy’s iPhone?
These are the questions that need answering.
Essentially: Clara isn’t just Clara, she’s every Clara. It’s all in her. In order to save the Doctor from the Great Intelligence in the Name of the Doctor, she scattered herself throughout time, constantly cropping up in the Doctor’s life and saving him from danger. Every time she had the same face, but her names varied slightly. The Clara we know best has the surname Oswald. The very first version of Clara the Doctor met (well, sort of, it’s complicated) was called Oswin Oswald. And Osgood is called Osgood, which is a bit like Oswin/Oswald.
It should be noted that this theory is wrong. Clara may have changed names, but she always had the same face. (Except when she was a Dalek, but let’s not get into that). Ingrid Oliver and Jenna Coleman do not have the same face. QED.
All we know for sure is we’re glad Osgood is coming home.