As an English name, Caleb came into use after the Protestant Reformation. It was common among the Puritans, who introduced it to America in the 17th century.
As an English name it has been in use since the Middle Ages, originally in the form Clare, though the Latinate spelling Clara overtook it in the 19th century and became very popular. It declined through most of the 20th century (being eclipsed by the French form Claire in English-speaking countries), though it has since recovered somewhat.
This name began rising on the American popularity charts in 2008, slowly until 2012 and then rapidly after that. This might have been triggered by the folk band Everly (not associated with the Everly Brothers), which had music featured on the television series One Tree Hill in that period. It also might have simply been inspired by similar-sounding names like Everett, Evelyn and Beverly.
A famous bearer was the American jazz musician Nina Simone (1933-2003).