Especially common as an African-American and Black-British name. The reasons for its popularity are not clear. It may well be a transferred use of the English surname Corey, which is derived from the Old Norse personal name Kori.
English: habitational name from any of the places named Welford, of which there are instances in Berkshire, Gloucestershire, Northamptonshire, and elsewhere. The first is named from Old English welig ‘willow’ + ford ‘ford’; the latter two seem to have the first element well(a) ‘spring’, ‘stream’.