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.
The spelling was later altered to Cordelia when Geoffrey's story was adapted by others, including Edmund Spenser in his poem The Faerie Queene (1590) and Shakespeare in his tragedy King Lear (1606).