Hi Becky,
Sunspots look like dark spots on the Sun, so "sun-spots".
I don't know who first used that term or first used it in English. The web page below describes early sunspot observations, and translates the title of a paper by Galileo
as "Three Letters on Solar Spots..."
http://galileo.rice.edu/s...ations/sunspots.html

Each particular sunspot group is also given a number, so we can distinguish them.
These numbers are given by the National Oceanic and Atmospheric Administration (NOAA).

Terry