A stan is a highly devoted fan of a particular person, like a musician, actor, author or influencer. The term comes from a song by Eminem, and stans often interact on Twitter [...]
It has been suggested the name "Stan" is a portmanteau of the words "stalker" and "fan", though it is unknown if the name was chosen with that intention. The term "stan" has since become an internet slang term for an extremely obsessed fan of something or someone and is derived from the song's title.
Let's take that etymology one step further: "fan" comes from "fanatic", so a stan is a stalker fanatic. Which somehow has become a positive term in some circles.