In the last day of the 2010s, the World Health Organization was notified by Beijing of a cluster of pneumonia cases in Wuhan, Hubei. This marked the beginning of the current COVID-19 pandemic.
Since May 31, 2021, variants of the virus are being assigned Greek letter names. It is quite conceivable that these will run out, and the WHO has already been looking for replacement names. Constellations are being considered, but out of the 88 officially recognized by the International Astronomical Union, at least some are unlikely to be used due to the WHO principles that the name must be unambiguous, simple to pronouce and non-stigmatizing (it is hard to conceive of it approving names like "Camelopardalis" or "Corona Australis" or "Indus", which means "the Indian", let alone zodiac constellations many people associate with their horoscope).
In any case, if the disease continues to be relevant one might imagine naming variants will continue to be necessary, with new sources for names being added as required.
How many named variants of SARS-COV-2 in its first 10 years?
The number in question is the count of officially-named variants in the series that, as of the time of writing, goes from Alpha to Omicron, skipping the letters nu and xi; if the naming for everyday use is later revised to include pre-Alpha variants on a par with Alpha and other letters, those are considered valid. Constellations or other sources of names also count.
The authoritative source shall be official proclamations by the WHO, or by any other agency that might be officially tasked with assigning worldwide names for variants for use by journalists and the general public, as opposed to systems geared towards scientists that pre-date even SARS-COV-19 itself.