In fact, she simply applies some minor cosmetic changes to her costume, like a stylized (bat-like) letter M instead of the batwings, and a denim miniskirt, and renames herself Misfit.
In truth, she only makes a few minor changes to her attire, such as swapping out the batwings for a stylized (bat-like) letter M and changing it to a denim miniskirt, and then decides to call herself Misfit.