Very rare as an American given name before 1980, it increased in popularity in the 1980s and 90s. It got a boost in 2004 after the debut of the television series Lost, which featured a character by this name.
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.