Jacobina sounds like a rebellion. Will make Tudors and Stuarts at school very interesting! Brings to mind carved heavy dark wooden furniture.
I know of an Andrewina, due to the Scottish tradition. She is not in the least bit posh, and usually tells people that she is called Andrina. The guffaws at her real name may have put her off it!
Binny a nice nickname??? Not to offend the poster who suggested it - but why would being called after a bin be good?
Ribena, beana, bin, etc would be very handy nicknames at school and the connection between beans and flatulence would be all to easy to make.