Can leaked nude pictures damage one's academic career? I have an ex who has posted nude photos of me online in the past, linked to my online social media, and posted my full name and where I live. I am concerned he may do so again once he finds out I'm now in a PhD program (he's very jealous of any success I have), and may link to my school bio page, or worse. 

Revenge porn is illegal in my state, and the case against him is currently pending. I have also gotten the photos taken down with a DMCA letter (I hold the copyright over the photos in question). At this point, I am concerned with how a future attempt could affect my career.  I can handle the embarrassment now that I've been through it once, so if that's the biggest concern, I can deal. I just don't want to lose a career over it, given how small academia really is and how a reputation might follow one around.

My question is, if I don't change my name (I've considered this, assuming I can keep him from finding out) and my photos are circulated and discovered by faculty or students, how likely am I to be thrown out of my PhD program or later lose a job as an untenured prof? Is a name change worth it? 

(If it makes any difference, they are essentially just topless portraits; I'm not engaged in any sexual activity or anything weird, and were taken 10 years ago when I was very young and foolish.)
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.