I bet Alya will come up with a good name for herself. Like others, I can't see her going with Volpina, as it would get confusing. In addition, the name has been tarnished. Because Volpina presented herself and could easily be spottable causing mayhem throughout Paris, everyone will associate the name with an akumatized villain. Alya, being so superhero-savvy, wouldn't want to reuse a name of a well-known villain; she'd want to give herself a new, fresh name that isn't a uncomfortable reminder every time she or someone says it. The ML Blog confirmed that "each Miraculous holder is able to choose their own name/superhero identity." Alya will make her own identity as a Fox Miraculous holder, something that isn't the same identity (and name) as a villainous Miraculous holder impersonator.
On Fox!Alya's powers, I have a hard time believing that Volpina's limitness ability to create illusions will be the exact power (or only power) that comes from the real Fox Miraculous. I'd love if tangible illusions or shapeshifting was the Fox Miraculous' superpower. With her flute, if she could blow some kind of magic/element out of it and possibly make a whip/sword/something else with it, like Melodie is seen doing in concept art, I'd be thrilled.