Why did Emilia give Subaru a fake name on the first time they met? On their first encounter on a timeline that was later reset, Emilia told Subaru her name was Satella. We then found out, after the first (or second?) reset, that that is the name of the Jealous Witch, and something of an insult to call someone else — Emilia reacted badly when Subaru called her out by that name after a reset and they hadn't yet met.

So why did Emilia tell Subaru that was her name that first time?
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.