According to Wikipedia, the English word 'cranberry' comes from the German kraanbere (translated as 'crane berry'). The word was first used in English in 1647, by John Eliot (1604–90) – an English–born missionary to the Native Americans, who used cranberries both as food and for dye.
'Fenberry' is one traditional English name for the closely–related plant that's more common in Europe; another, according to the Online Etymology Dictionary (OED), is 'marshwort'. They were used in cooking by European colonists as early as the late 17th century; the OED states that they were exported to Europe from around the same time, and by the 18th century the native European berries were being referred to in English as cranberries.
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