Georgina (GHE-or-ghee-na) is also used in Hungarian. Györgyi is very old fashioned, it's easily confused with Gyöngyi (=pearl), and Györgyike sounds ridiculous on an adult.
This name is relatively popular in the UK, but quite rare nowadays in the US. This is probably because George and its other feminine variants are much more popular across the pond. In 2012, 113 American baby girls were named Georgina.