Seems like a good call.
"The South Africa Variant," "The Brazil variant" are especially like the "Spanish flu," where it's just named those names because that's where it's been studied first and with good research & funding. The US certainly has had dozens or hundreds or thousands of variants over the last 15 months, given that we were the worst country in the world for COVID-19 we'd be the source of a lot of new variants, but because we largely weren't doing the sort of research we needed to be doing discovering new variants, we didn't name many new variants as "The American Variant." When we did, it was mostly just after cities and states that funded and had organized research in tracking new variants... so you had "The New York Variant" and "The LA Variant," but those variants were discovered during relatively benign periods of viral outbreak (relatively...). Meanwhile, we never named a "North Dakota Variant" because nobody in North Dakota was doing shit to track variants, even though North Dakota is literally one of the worst hit places in the world for COVID-19.
Also very very very good call on not naming the variants after Greek gods. We don't need the Dionysian Variant of COVID-19 in our social consciousness.
The official names are going to be ... B.1.1.7 and so on, but in the popular sphere they'll push "Gamma Epsilon" or something, so that people won't inevitably call these "The Indian variant" or "The Bolivian variant" or whatever, which just begs to be misunderstood.