I don't know where you got the information that Jaana is related to Jane or any other variant of Johannes. Instead it has been used as a short form of several names ending with -jaana or -iaana, like Marjaana, Ottiliaana, Juliaana. Nowadays it is considered as a short form of Marjaana, with which it has been placed to the Finnish almanac (August 15th). [noted -ed]