"A/B testing" is defined as "a method of marketing testing by which a baseline control sample is compared to a variety of single-variable test samples in order to improve response rates".

The point here, of course, is to know which small single-variable changes are more optimal, with the goal of finding the local optimum.

However, one can also envision a somewhat related but different scenario for testing the response rate of major re-designs: take a baseline control design, take one or more completely different designs, and run test samples on those redesigns to compare response rates.

As a practical but contrived example, imagine testing a set of designs for the same website, one being minimalist "googly" design, one being cluttered "Amazony" design, and one being an artsy "designy" design (e.g. maximum use of design elements unlike Google but minimal simultaneously presented information, like Google but unlike Amazon)

Is there an official name for such testing?

It's definitely not A/B testing, since the main component of it (finding local optimum by testing single-variable small changes that can be attributed to response shift) is not present. This is more about trying to compare a set of local optimums, and compare to see which one works better as a global optimum. It's not a multivriable, A/B/N or any other such testing since you don't really have specific variables that can be attributed, just different designs.