Yes you can. They [recommend you apply for a new visa with a name change](https://travel.state.gov/content/travel/en/us-visas/visa-information-resources/frequently-asked-questions/about-basics.html).

> If your name has legally changed through marriage, divorce, or a court
> ordered name change, you will need to obtain a new passport.  Once you
> have a new passport, the Department of State recommends that you apply
> for a new U.S. visa to make it easier for you to travel to and from
> the United States.

[Executive Order Suspends (at Least Parts of) the Visa Interview Waiver “Dropbox” Program
](https://www.cilawgroup.com/news/2017/02/02/executive-order-suspends-least-parts-interview-waiver-dropbox-visa-stamp-program/)

 However note that via [Executive Order 13769](https://www.federalregister.gov/documents/2017/02/01/2017-02281/protecting-the-nation-from-foreign-terrorist-entry-into-the-united-states), President Trump suspended a good portion of the Visa Interview Waiver “Dropbox” Program which is same as visa renewal. 

This means many people who hitherto could just renew their visas without interviews are now subjected to interviews thus be prepared with all the necessary documents to be interviewed in case you are called up.

**Choose YES**. They will make the determination if they want to interview you.