There is Bargoine (Bernard) and an old English name Bregowine. Maybe
Bargowine was spelt as the Vicar heard it, or it is a mistranscription by the
person who forwarded it to the IGI (I note the entry is not an extraction
reference on the igi site).
The suffix 'ine' or 'ina' is usually added to a male name when the child
a girl, eg Thomasina, Josephine.
Hope you find out more.