Did they fuck with us?
Surely the name of the Doctor is the Doctor.
He evidentially has many, many names.
But the name they focussed on this episode was the Doctor even if his given flashed us from off camera.
The episode was about "why" is the Doctors name Doctor and not "what" is the Doctors other name.
The Splintered Clara's... lets assume that some of them knew th nature of the game they were playing and others were fricking clueless.
The Girl in the shop might have been Clara.
Susan walks into the Tardis they are stealing, then Clara says "not that one, this one..." the Doctor pivots and takes the right TARDIS accidentally abandoning Susan on Gallifrey.
The Doctor went joy riding with the master remember.
Maybe the Doctor stole a lot of TARDISs?