Tucked away behind the door (ajar) of the chemistry lab (empty), Sherlock makes a mental note to check her file again later. He suspects that was a lie, but he prefers data to suspicions.

He doesn't see her face. Perhaps another day; no need to rush.

Aware of Tony's charming inability to hide even the simplest of facts, he divulges nothing, not even her full name. Not that Tony asks. You could power a small city with the force of Tony not asking.