Klingberg can be both a middle name and a surname. Notable people with the name include:
Middle name Peter Klingberg Geschwind, Swedish contemporary artist
Surname Bertha Klingberg, German florist Börje Klingberg (born 1952), Swedish speedway rider Niklas Klingberg (born 1973), Swedish speedway rider, son of Börje Carl Klingberg (born 1991), Swedish ice hockey forward Christian Klingberg, Danish attorney David Klingberg, Australian businessman, civil engineer, and chancellor John Klingberg (born 1992), Swedish ice hockey defenceman Marcus Klingberg, Polish-Israeli epidemiologist Mårten Klingberg, Swedish actor, screenwriter, and director Niklas Klingberg (footballer) (born 1985), Swedish football defender Torkel Klingberg, Swedish cognitive neuroscientist