As a given name, it was used on the American sitcom Murphy Brown (1988-1998) for both the mother and son of the main character. By 1998 it was more popular as a name for girls in the United States, perhaps further inspired by a character from the movie Jerry Maguire (1996).
This name was fairly common in France, England and the United States in the early 20th century. It became quite popular in France and England at the end of the 20th century, just when it was at a low point in the United States. It quickly climbed the American charts and entered the top ten in 2014.
In England Oliver was a common medieval name, however it became rare after the 17th century because of the military commander Oliver Cromwell, who ruled the country following the civil war. The name was revived in the 19th century, perhaps due in part to the title character in Charles Dickens' novel Oliver Twist (1838), about a poor orphan living on the streets of London. It became very popular at the beginning of the 21st century, reaching the top rank for boys in England and Wales in 2009 and entering the top ten in the United States in 2017.