"Peter has a show!"
Translation:Péternek műsora van!
Both are correct. Your version puts the emphasis on Péter (or possibly van.) With the exclamation point, I'd say that "Péternek műsora van!" is more natural, though.
So 'Péternek műsora van' is like Peter has a SHOW, and 'Péternek van műsora' is PETER has a show/It is PETER who has a show?