In the comics, Thor, our beloved Thor becomes unworthy to wield the Mjolnir. But, there has to be a God of Thunder. So, Jane Foster is chosen as the new Thor.
Following that, our old Thor, the guy – starts calling himself as Odin-son and gets into trying to figure out the identity of this new Thor.
I have liked this idea of Thor becoming unworthy and someone else getting to wield the Mjolnir. So, here we have our new God of Thunder – still called Thor. No She-Thor or Thoress or anything like that.
At one point, Odin-son suspects Jane Foster to be Thor, and at that time, Mjolnir uses it’s magic and appears as a hologram of Thor. Assuming that hologram to be the real Thor, Odin-son stops suspecting Jane and continues his search.
It is very interesting how the hammer’s magic is used in that scene. It has never been shown to be able to do such things before and Jane herself doesn’t know how the hammer did it either.