This isn't to argue whether or not Logan takes the name again. This is if Laura stays Wolverine. Also how is she taking someone else's legacy, when SHE IS that legacy. She took on the name, because she felt as long as she wore cowl and mask, he would never be gone.
As well, she's made significant strides in her book becoming less of the near-emotionless, machine-like killer she was back when she started on the X-men and later joined X-Force. She's becoming more human (in good way).