What is the elephant family name?

Elephants do not have family names, only species names. The three extant elephant species are known by their scientific names: Loxodonta africana, Loxodonta cyclotis, and Elephas maximus. African bush elephants are in the species Loxodonta africana; African forest elephants are in the species Loxodonta cyclotis; and Asian elephants are in the species Elephas maximus.