What's in a Name?
It's heartening that the OP is trying to turn their life around and start afresh. However, their wife deserves to know the full story of the person she married. Ideally, such conversations should occur before marriage – before choosing a last name becomes an issue.
Nevertheless, honesty is crucial, and it's better late than never. Come clean with this woman, OP. Hopefully, she will appreciate the transformation into the law-abiding individual she knows you to be.