She was attempting to hide her true intentions, but slipped up.
Wanda: What if you brought America here?
Strange: Here?
W: Yeah. I know what it’s like to be on your own, hunted for abilities
you never wanted, and I can protect her.
(SUSPENSEFUL MUSIC PLAYS)
W: You never told me her name, did you?
Strange Picked up on it almost immediately, and she revealed herself by mistake. She obviously didn't want to attract attention to herself, because then that would create more hassle - having to deal with everyone trying to protect America, instead of just hunting America down on her lonesome. So now she had been discovered, what would the point be of hiding the truth further, as it would only cause more problems. Best reveal herself and her intentions: She only wants one person, there's no need to involve any one else. She knows Strange is all about balance, so maybe he would understand.
And then, as WakeDemons3 has commented
It sets the audience up for a visual matching the reveal of her as the bad guy.