My real name is Katja, which has given me a pretty interesting entry into the world of Russian diminutive names and some of the divinative forms developed from my name are also in Finnish and Karelian.
In Finnish and Karelian I have always been called Katjuska. Some have said Katjuusa, which is popularized by Finnish cover of Katyusha called "Karjalan Katjuusa" (engl. Karelian Katjuusa).
In the Orthodox Church, you refer yourself with saint's name so I am Jekaterina.
I've been called Katyusha, which is a pretty funny, cute and badass name because it has a kind of tension between cuteness and fear, because in the Russian cultural context, Katyusha also refers to the rocket launchers of the same name that defeated the Nazis.
If I have to say my name in Karelian, it will be written as Katjoi. Of course, no one would be upset if I introduced myself as Katja in Karelian, but of course people appreciate using a Karelian name in the Karelian language.