Sim Mayor said: So maybe it comes down to whether there is anybody else capable of the role. In Jane's case, Thor is unworthy and so she takes on the concept of Thor even though he is still around. And let's not forget Eric Masterson. Thor was stripped of his godhood and thought dead, so Eric assumed the mantle for a good long period without anybody claiming he wasn't really Thor.
So maybe it comes down to whether there is anybody else capable of the role. In Jane's case, Thor is unworthy and so she takes on the concept of Thor even though he is still around.