Word for answering the question you wish had been asked not the one asked?

To equivocate is "to avoid committing oneself in what one says."

To prevaricate is "to avoid telling the truth by not directly answering a question."

A hedge (or to hedge) is "a calculatedly noncommittal or evasive statement."

To beat around the bush is "to fail or refuse to come to the point in discourse."

All definitions from merriam-webster.com.

You have already mentioned dodging. Apparently, this is as concise as you can get without going into motivation and specific techniques, and, even among the academics, there is no better highfalutin word or phrase for it.

Take this paper, for example - The Artful Dodger: Answering the Wrong Question the Right Way from the Harvard School of Business (this is a review version, with reviewers comments included).

The authors of the paper, and the reviewers as well, are very comfortable with using the word dodging to describe the act of responding to a question with an answer to a different question.

What happens when people try to “dodge” a question they would rather not answer by answering a different question? In four online studies using paid participants, we show that listeners can fail to detect dodges when speakers answer similar – but objectively incorrect – questions (the “artful dodge”), a detection failure that went hand-in-hand with a failure to rate dodgers more negatively. We propose that dodges go undetected because listeners’ attention is not usually directed at a dodge detection goal (Is this person answering the question?) but rather towards a social evaluation goal (Do I like this person?). Listeners were not blind to all dodge attempts, however.

Dodging remains the term used throughout the paper and even within the (presumably august) reviewers' remarks.

Other terms are mentioned in the paper, but they are more about theory and motivation. These terms include Gricean conversational implicature, Information Manipulation Theory, Interpersonal Deception Theory, and intentional blindness. But these aren't substitutes for dodging. They only serve to provide context for specific studies on dodging.

If you need to qualify the term in context, then question dodging is a more complete way of saying it.

Second answer, not related to original answer, so I've re-posted.

I found an NPR piece on exactly this subject. The people who train the politicians to do so, call it a Debate Pivot.

The journalists who ask the questions call it a dodge.

I'm not certain that either is quite the formal term you are looking for. But, the fact that the people who train others on the subject refer to it as a debate pivot would be good enough for me.

I think two words that are used to describe this sort of interaction are sidestep and circumvent.

to manage to get around especially by ingenuity or stratagem