'Covent' is Anglo-French for a religious community, a 'convent'.
By 1200 the Abbot of Westminster Abbey had walled off land here for fields and orchards; a document of 1250–1283 calls it 'the garden of the Abbot and Convent of Westminster'. A lease of 1515 names 'a garden called Covent Garden'. In 1552 Edward VI granted it to the Earl of Bedford. The fruit and vegetable market, there by 1654, moved to Nine Elms in 1974.