He leans in to change his persona...see up until that point he was suave and charming. She showed him an IOI by not only laffing at his joke, but then countinueing the role play by asking "what that would look like"....so he showed her what a genuine guy would look like by emulating it in his body language (leaning foreward to show hes invested in the convo), and by introducing himself. Now she doesnt see him as the same guy, its as if he pealed the "cool" away to give her a glimpse of his real side. Essentially frame control...it is possible to be too smooth and cool, thus blowing the frame.