As an English name, Benjamin came into general use after the Protestant Reformation. A famous bearer was Benjamin Franklin (1706-1790), an American statesman, inventor, scientist and philosopher.
Because Elijah was a popular figure in medieval tales, and because his name was borne by a few early saints (who are usually known by the Latin form Elias), the name came into general use during the Middle Ages. In medieval England it was usually spelled Elis. It died out there by the 16th century, but it was revived by the Puritans in the form Elijah after the Protestant Reformation. The name became popular during the 1990s and 2000s, especially in America where it broke into the top ten in 2016.
The name was common in France during the Middle Ages, and was introduced from there to England, though it eventually became rare. Interest in it was revived by the character Melanie Wilkes from the novel Gone with the Wind (1936) and the subsequent movie adaptation (1939).