Sigma had chosen that name because it was familiar enough that he would react to it, and this intended effect backfires on him spectacularly: he raises his head to look her in the eye as 'she' calls his pseudonym. Then, he goes white.

"That's not my name," he coughs, pretending to be confused as he returns his gaze to her leg, ripping open the first aid kit with a clatter. He is glad the light is dim enough that she can not see him slowly turn red. How horrible it would be if she thought of him as some dirty old man!

The Doctor falls for Rat's trick even without the makeup or gown.Only the women were given one-pieces, he believed, and Sigma does not think twice. "..I have to take your leg. Is that alright?"