Can leaked nude pictures damage one's academic career?
I think you can generally trust faculty to be adults when it comes to graduate admissions and a tenure track job. 

The biggest problem I would see is when you teach (future undergraduate) students. I'm not sure how you would want to deal with them. 

I would say that university administrators tend to be adversity shy and could be a problem.  

I would instead look to see if a lawyer might help you DMCA the sites hosting the images as well as file either a legal complaint or restraining order against you ex.  This latter bit is best asked on Law Stack Exchange. 

University registrars and faculty are used to students having to change their name due to a variety of circumstances. You should be able to get new transcripts and letters issued under your new name without issue. But the abuser can also link images to your new name unless you can prevent him or he loses interest; so a name change is not a foolproof solution.