PDF link: https://apps.who.int/iris/bitstream/handle/10665/163636/WHO_...
> Disease names may NOT include: Geographic locations
> Examples to be avoided: Cities, countries, regions, continents
Why this is not applied to “the $country variant” is a very good question.
Now is a different situation, the whole world is now a part of the pandemic. The phrase "the UK variant" or "the Brazil variant" is much less likely to negatively effect people.
I suspect that if a scientist had called it "The Chinese Virus" or "The Wuhan Virus" no one would have thought twice about it. They probably did too.
Was it? "called" In what way? In tabloid headlines maybe. But that was never a formal name for COVID-19, because formal disease names don't work that way. See "World Health Organization Best Practices for the Naming of New Human Infectious Diseases" (2015) Link above.
You can call that "PC reasons" if you like, but IMHO that's trivialising the use of existing agreed best practices, that exist for good reasons. As others here have pointed out, if a politician prefers to say "Wuhan virus" or "China Virus" over "COVID", then they are deliberately using a loaded term for xenophobic purposes.