The devotional verb stan begins appearing in 2008 as a generalization of the noun stan. The noun originates from a 2000 song by Eminem, titled “Stan”, about an encounter with an eponymous obsessive fan. This usage didn’t start catching on until after 2005, but by 2015 it was notable enough to merit an entry in the OED’s blog. By 2017, it warranted a full entry in the big dictionary.

As a given name, Stan is short for Stanley, which seems to mostly originate from places named Stanley in England. Stanley is Old English for “stone meadow” (stān + lēah), which seems like a reasonable name to give to a bunch of different places.