Well. Rita was smarter than he gave her credit for. Strange expected someone more closely aligned with the fae to point out his specific wording in the binding spell, not a changeling in a biker gang (because really, that's the only place he can think of in their conversation where he hinted working with someone else). Strange can't help but give her a little impressed nod.

"I can't tell you--and don't try to hit me again, it won't be any use! We cast a binding spell as well, I'm not going to risk the backlash by telling you her name."

Granted, faerie contracts aren't binding spells...but at least in Strange's mind, they're probably worse. The agreement with Nightshade was that they wouldn't betray each other, Strange is taking all the precautions known to man. Telling Rita that he plans on sharing his findings with a woman is as much as he's willing to bend.