That word is "Stan."Here is how the dictionary defined the word:
An overzealous or obsessive fan of a particular celebrity.
While obviously the name Stan has been around forever— shout out Stan Lee — Stan, in the context of someone acting obsessively over someone, was birthed by Eminem. In 2000, Eminem released the now-classic single "Stan," a song about a depressed, "overzealous" fan who writes a number of crazed, obsessive letters to the rapper.