I really enjoyed the Servant too, but the one I watched was also about a couple who had a baby die, and the wacko mom followed this therapy that involved having her care for a real doll / baby doll as part of her recovery, and then they hire a nanny to help care for the doll, then the doll comes to life. Freaky M Knight Shamalamadingdong story writing. I didn’t see any adults assuming another identity though.
Edit – didn’t read far enough before replying. I see now you were talking about The Serpant.