"I haven't been stubborn about it." She just hasn't given it yet, despite Joker already asking, because she doesn't feel like it. She's pretty sure that's not the same as being stubborn.

That said, even if she hasn't bothered so far... she guesses she might as well tell this girl her name now. Even if she turns out to be lying about trading it for the item, it's not like it'll be a huge loss, and Ginko can still fight her for it.

"...It's Ginko."