If you look at Coronavirus in Wikipedia, you might note the classification section:
lists Alphacoronavirus, Betacoronavirus, Gammacoronavirus, and Deltacoronavirus. These have nothing to do with the recent designation of four variants as Alpha, Beta, Gamma and Delta. SARS-CoV-2 and all its variants are part of the Betacoronaviruses.
Using Greek letters for the variants is a bad idea. There’s going to be lots of confusion going forward where people google “alpha coronavirus” and get something they aren’t looking for.
Anyway, if you’re already confused, the four variants were previously known by where they were first found:
Alpha – first found in the UK
Beta – South Africa
Gamma – Brazil
Delta – India