I am not a member of the solar section, nor am I an expert on these matters. You may want to look here though:
I’ve seen reference to a formal naming system for sunspots. Where can this be found?
There is no naming or numbering system for sunspots. There is a system for numbering active regions, however. An active region can contain one or more spots. The National Oceanic and Atmospheric Administration (NOAA) numbers active regions consecutively as they are observed on the Sun. According to David Speich at NOAA, an active region must be observed by two observatories before it is given a number (a region may be numbered before its presence is confirmed by another observatory if a flare is observed to occur in it, however). The present numbering system started on January 5, 1972, and has been consecutive since then. An example of an active region “name” is “AR5128” (AR for Active Region) or “NOAA Region 5128”. Since we only see active regions when they are on the side of the Sun facing the Earth, and the Sun rotates approximately once every 27 days (the equator rotates faster than the poles), the same active region may be seen more than once (if it lasts long enough). In this case the region will be given a new number. Hence, a long-lived active region may get several numbers.
On June 14, 2002, active region number 10000 was reached. For practical, computational reasons, active region numbers continue to have only four digits. Therefore, the sequence of numbers is 9998, 9999, 0000, 0001, and so on. Active region number 10030, for example, is AR0030. This region will often simply be referred to as region number 30, with 10030 implied.