Recorded as Fibben, Fibbans, Fibbens, Fibbins, Fibbings, Phibbens, and possibly others, this would seem to be an English surname. It is quite rare and does not seem to appear in any of the known directories of surnames of the British Isles. It is however reasonably well recorded by the International Genealogical Index for the city of London from Elizabethan times and particularly during the 'reign' of Oliver Cromwell (1650 - 1658). In our opinion its origins are the Olde English or Welsh personal name 'Iben' fused with the medieval patronymic 'Ap', this being cognate with the Scottish and Irish 'Mac' or 'Mc' and meaning 'son of Iben'.Unfortunately we cannot prove this origin as we have not been able to find an very early link spelling, but nor have we been able to find any other explanation. The first known recording would seem to be that of Christopher Fobyn who married Elizabeth Wolverstone at Uxbridge in Middlesex, on May 18th 1572, and John Fibbens and his wife Dorcas, who were christening witnesses to their daughter Sarah at St Dunstans in the East, Stepney, on August 12th 1652.
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