Why did Emilia give Subaru a fake name on the first time they met?
At about 11:00 in Episode 8.


  Beatrice explained the Jealous Witch to Subaru when talking about Subaru's "Witch Smell" in the library. Beatrice says only mad people will pretend to be the Jealous Witch. Suddenly, Subaru figures out the reason why Emilia pretended to be "Satella".
  
  That is because she didn't want someone else to get involved in the Throne Fight, with her special appearance, pretending to be the Jealous Witch is the fastest way to scare people away.
  
  But the plan actually failed because Subaru is a man from another world where the tales of the Jealous Witch doesn't exist.