The most famous doll in the world was named Barbie because it was the name of her creator’s daughter. However, she has a (different) full name: Barbara Millicent Roberts.
The name (as well as the ones of Barbie’s parents, George and Margaret Roberts) first appeared in a series of novels published by Random House in the ’60s. In them, the family lived in the fictional town of Willows, Wisconsin and Barbie attended Willows High School, while in the Generation Girl books, published by Golden Books in 1999, she went to the fictional Manhattan International High School in New York City (apparently based on the real-life Stuyvesant High School).
Her boyfriend Ken also received a last name: Carson.