Kurama and Hiei are both mountains in Japan.
Botan's name is a joke, a reference to the length of the sleeves of her kimono. Botan, in Japanese, means sleeves or cuffs on clothing.
Yusuke's last name, Urameshi, is pronounced Yur-a-mesh-i throughout the English dub of the show, while it's supposed to be pronounced, Oo-ra-me-shi.
While the title of the series literally translates as "White book of Melancholy", or "White book about Ghosts", it was changed to Poltergeist Report and Ghost Files to be more catchy for American audiences.
Yusuke's first name means "ghost helper" and his last name Urameshi is a word that is said by dead spirits.