 Geva was born in St. Petersburg, Russia, with the surname Zheverzheeva, sometimes spelled Gevergeyeva (), the daughter of Tamara Urtahl (who was Swedish) and Levko Zheverzheev (or Gevergeyev).Geva's paternal grandparents, founded a business, which their son inherited, which manufactured objects for the Russian Orthodox Church, including precious icons and ornaments, as well as gold lame and lace for church vestments.Geva's parents were patrons of avante-garde artists.