His free hand is right there to catch her by the upper arm. To stabilize her, of course. Though said stabilizing apparently is an ongoing process, given that he displays zero interest in letting go.

And her name? Oh, buddy.

Joker snorts, actually snorts, then begins to chuckle. "You know, when most girls give a guy a fake name, they choose some sort of liquor or fruit." The look in his eyes softens slightly, amusement tempering the darker elements. "'Brandy,' maybe. Or 'Cherry.'" How many singles has he tucked into the garters of Cherries, he wonders?

"But you. You!" He chuckles again, then gives her a wink. "You sure you don't want to try again? Be a 'Diamond' or an 'Eden,' perhaps?"