Rasmussen was born in 1953 in Ginnerup, Jutland, to farmer Knud Rasmussen and Martha Rasmussen (née Fogh). His surname is Rasmussen, while Fogh, his mother's maiden name, is his middle name and not considered part of his last name. He is correctly referred to as Rasmussen (not Fogh Rasmussen), unless his full name (including his given name) is used. In Danish media and society, he has often been popularly referred to as Fogh Rasmussen, or merely Anders Fogh, when not referred to by his full name, mainly to distinguish him from other prominent politicians in the country with the same family name.