I have a valid US visa with my maiden name. My full name has changed after marriage. I have got a new passport with my new name. I have to travel and its suggested to apply for a new visa. On the new visa application appointment scheduling shall I say YES to the Questions that says 'Do you have a valid visa?'
Saying yes, it is considered as renewal. Can I apply for renewal visa in my new name on basis of my valid maiden name visa?
Yes you can. A name change does not invalidate a USA visa and from their own language you can continue to use it. They recommend you apply for a new visa with a name change just for ease of travel.
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
However note that via Executive Order 13769, 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.