The show is set in Nanba Prison. "Nanba" means "Number". Most of the characters are named after numbers.
The series title "Nanbaka" is a portmanteau of the Japanese words "nanba" (after Nanba Prison) and "baka" (fool).
Three Nanba prison guards - Kiji Mitsuba, Kenshirou Yozakura and Samon Gokuu - are named from a Japanese folktale about Momotaro, a folk hero born from a peach, who befriended a pheasant, a dog and a monkey (respectively "kiji", "ken" and "samon" in their names). Mitsuba, Yozakura and Gokuu serve under Momoko Hyakushiki, who is named after a peach ("momo"), and each has decorations on their uniform referencing a bird, a dog, and a monkey.
The Daisen brothers Rokuriki, Kokoriki and Youriki are named after "roku", "koko" and "you" (the Japanese words for 6, 9 and 8) and "riki" (the Japanese word for "power").
Nanbaka broadcaster Mitsuru Hitokoe is named after "mitsu" (the Japanese word for "3") and "koe" (the Japanese word for "voice").
Three Building 5 guards are named after some of the main characters in the Chinese epic "Journey to the West": Samon Gokuu is named after Goku, the Monkey King Inori Hakkai is named after "i" (Japanese for "wild boar"), which represents the pig monster Houzoku Sanzo is named after Genjo Sanzo, a Buddhist monk.