Board Thread:Questions and Answers/@comment-120.29.104.46-20180826143229/@comment-33994734-20180826233212

I'm pretty sure the answer must be somewhere in the comments.

Emilia didn't want Subaru to get caught in her problem because she needed as few people as possible to know she'd lost the isigna (since people would think someone who can't look after an isigna could not possibly look after a whole country).

And so, as someone who's appearance matches that of the legendary Witch of Jealousy, she thought telling him her name was Satella would destroy his will to help her.

Of course once he died the world was reset back to before she had the idea or any reason to tell him her name was Satella, and so calling her that was really offensive to her partly because she knows that's what people think when they see her.