I still have problems with these type of things.
I think I understand well that between "I know where the house is" and "I know where is the house" the correct sentence is the first one (I hope so). But in the title's case I'm not sure at all.
I don't know who Sophie is.
you are saying that you are not familiar with Sophie.
I don't know who is Sophie?
Sounds awkward to a native ear, but is understandable. Better might be
I don't know. Who is Sophie?
In which you are asking the question seeking information about Sophie.
Generally, the question will imply that you are not familiar with Sophie and has the same implicit meaning as your other sentence, but the question is seeking information about Sophie where as the other sentence is only saying you do not know Sophie.
P1: Is Sophie the new student?
P2: I don't know. Who is Sophie?