A shortening of the name Virginia, pronounced Gin(like the drink) followed by a hard "E" sound. It is also (and more commonly) spelled Ginny. Not to be confused with Jenny, which is a shortening of the name Jennifer.
My name is Virginia but everyone calls me Gini.
My name is GIN-E not Jenny or Jen or Gina. And it's short for Virginia not Jennifer don't make assumptions they usually just make you look stupid and/or rude.