Emilia could really be Satela, as it's the first name she presented herself in the first ep.
Then Subaru died and the setting changed.
But Subaru and we remember.
I doubt she's Satella when Rem can see witch aura. If she was used to it she wouldn't be killing Subaru over it.

Puck said "You've got bad taste" when Emilia introduced herself as Satella. She cheekily used it to fool around with Subaru.

It would also seem very very odd for the Witch Cult to kill the witch.