Eminem's definition of "Stan" is now Oxford-approved.
Rewind to 2002 when Slim Shady released the Dido-assisted track about an overzealous fan named Stan who writes a letter to the Detroit rapper. As Exclaim! points out, the Oxford English Dictionary has plucked his version of the word, defining "stan" as both a noun ("An overzealous or obsessive fan of a particular celebrity") and a verb ("Be an overzealous or obsessive fan of a particular celebrity").
The dictionary also lists the origin of the word as "Early 21st century: probably with allusion to the 2000 song “Stan” by the American rapper Eminem, about an obsessed fan." Even the OED's sample sentence for the noun makes a reference to a "rap god," which was the title of a 2013 Eminem song: "He has millions of stans who are obsessed with him and call him a rap god."