This name has been used occasionally in England since the 12th century. It was not common in the English-speaking world until the end of the 20th century.
As a rarer (but older) masculine name it is probably derived from a surname: see Fay 1 or Fay 2.
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.
This name experienced a rise in popularity at the end of the 20th century. It was the most popular name for girls in England and Wales from 2011 to 2015.