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Type Surname (from nickname)
Nickname for a lighthearted or cheerful person, from Middle English, Old French gai.
Type Surname (from location)
Habitational name from places in Normandy called Gaye, from an early proprietor bearing a Germanic personal name cognate with Wade.
Type Surname (from given name)
Probably from the Catalan personal name
Gai. (Catalan form of the name
Gaius).