There's a few names that can work. Shifter, Double, Mimic, Gemini, Doppleganger, Anonymous, and Sapien spring to mind. You can come up with a sufficiently cool name if you think long enough. 

I like the sheet, but there are a few issues with powers. If she's a shifter she shouldn't change into anything that's inorganic, she should feel pain maybe have higher tolerance but she should have working nerves, and she should only be any faster or more agile if she crafted a body that was naturally quicker. And even then it shouldn't be anything superhuman unless she turns into an animal or something. 

And for her kleptomania that one would have to be a secret otherwise she'd get in a bit of trouble, or else find another profession. And yeah the ending could use an an explanation for why she would join the League.

Arty, Yep Rolling Girl is accepted. Again :P Though if she ever finds a cooler name changing to it will not be disputed haha. 

Would she be back in at the start of the RP or join shortly after? 

Didn't you talk about making a second as well?