As viruses go, it's not a rapid mutating virus (flus and common colds are usually worse). But it does mutate at a systematic rate, all on its own, just as every piece of DNA and RNA can do. Here's a recent phylogeny (map of mutant strains of COVID):
auspice
Note that it's the "20" series that's now the most prevalent in the world, while the original "Wuhan" strain is less prevalent/therefore has fewer mutations going on.
That 20 series is the "more infectious" strain that appeared early on (I haven't researched it recently, but it was noted in the French alps and in Northern Italy before arriving by February IIRC in New York.
Then, we have other mutations (more recent) where it's alleged that these mutations also make COVID more infectious (more enduring in the air, more virions exhaled per breath, etc). This isn't known for sure because the social conditions in the places of origin were so chaotic (so many people not wearing masks, people using public transport, etc) that it could simply be an ordinary viral dynamic. Anyway, nextstrain.org is a fascinating place to learn about the virus.
Just rest assured that the vaccines are still effective unless and until more mutations occur in the spike protein encoding part of the RNA. I think there's also good evidence that people who had any previous form of SARS have increased immunity/a milder case with this one.
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