Digress? obfuscate? pivot? approach avoidance? pragmatic topic loss?

A broad heading for such tactics is:

dodging/dodging the question/question dodging

dodge

To evade (a question, charge, etc.) by trickery, cleverness, etc. Webster's New World

If you dodge something, you deliberately avoid thinking about it or dealing with it, often by being deceitful.

dodge the question

He dodged the question. The Sun (2010)

Nor does he dodge the awkward question - whether smaller schools can be justified economically. Times, Sunday Times (2008) Collins

Question dodging

Question dodging is a rhetorical technique involving the intentional avoidance of answering a question. This may occur when the person questioned either does not know the answer and wants to avoid embarrassment, or when the person is being interrogated or questioned in debate, and wants to avoid giving a direct response. Wiki

A lot of the other coaches, when I asked them about playing quarterback, they'd hem and haw. They'd dodge the question. ref.

In practice there are are variety of ways of performin covert question dodges. For example, if the political figure is asked a specific question, that is a question about some narrow issue or point, then he or she may skirt around it by giving an answer to a more general question concerning a broader topic... ref.

(I also see ducking a question.)

The OP asks "What is the name and what is the problem?"

I believe dodging is the name. Analyzing the problem could take us far afield of ELU :-)

The common word for this is deflection. The easiest way to find examples is to google the word, followed by the name of a politician or someone else whose name is currently linked with some scandal.

Here’s a headline example from MSN: https://www.msn.com/en-us/news/politics/greg-abbott-s-demagoguery-and-deflections-are-putting-texans-at-risk/ar-BB1ej1W8