These are from the PANGO lineage designation system (https://www.pango.network https://www.pango.network). They're based on the inferred phylogeny (i.e. family

These are from the PANGO lineage designation system (https://www.pango.network https://www.pango.network). They're based on the inferred phylogeny (i.e. family tree) of the various variants. Variant B.1.1.529 (not BA.1.1.529 -- that's a mistake in the article) is descended from B.1.1, which is descended from B.1, which is descended from B (which is the first haplotype that was detected). More specifically, B.1.1.529 is the 529th descendant of B.1.1 that the pango group have assigned a number to; it has no particular relation to B.1.1.528. So what about "BA"? To keep these sequences from getting too long, they assign aliases, and BA is the alias of B.1.1.529 (they ran out of single-letter prefixes a while ago). So BA.1 is short for B.1.1.529.1, and BA.2 is short for B.1.1.529.2, etc. (And since these are all in the Omicron family tree, they're all classed as Omicron subvariants.) Similarly, the original Delta variant was B.1.617.2, which was assigned the alias AY, so AY.1 (=B.1.617.2.1), AY.2 (=B.1.617.2.2), etc are all Delta subvariants. The current full lineage list is available at https://cov-lineages.org/lineage_list.html https://cov-lineages.org/lineage_list.html. Note that they're tracking variants in far more detail than any non-virus-nerd cares about. If I'm counting right, there are 1575 non-withdrawn lineages listed, including 210 in the Delta family.