In elementary school (4th grade, specifically), I had a classmate named Dejana, and she was originally from Bosnia--though her English was perfect, and you'd think she was a naturalized American. But I'm pretty sure she was an immigrant. Anyway, she pronounced her name the same way you would pronounce Deanna, being dee-AN-uh. I always thought her name was really pretty.
No, that is not how Slavs would pronounce it. I am Slavic and have lived in a Slavic country all my life. For all you know, the girl could've been born in an English-speaking country and just never have bothered with learning the right way to pronounce her name, or pronounced it the "English" way so as to not confuse people.