Well, this issue is a problem I also deal with ever since I have followed Greta's results. What's her orgin? Is she a member of a mixed family? (her mother's name is obviously Katalin - being a human being of german heritage I can't judge wether this is a real hungarian name, but I guess so). Her father (Rudolf) seems to be german and her brother (Norbert) owns a german name. Possibly Greta might have a double citizenship?
Well, according to her interview about the subject: She was born in Budapest, her father is german, her mother is hungarian. She and her family lived in Budapest for a while, then her father got a new job, so the whole family moved to Germany. She became a tennis professional in Germany, so she played for Germany of course. A few years ago the family moved back to Hungary, they live in Budapest.
Greta does have double citizenship, and according to the interview, she considers herself as both German and Hungarian. But since she lives in Budapest for a while now, she feels her "hungarian side" become somewhat stronger - if this is the right word for it?. And for this reason, she decided to represent Hungary in the future.
Anyway, she seems to be a lovely girl, so I wish her the best luck in her carreer.
(Yes, Katalin is a hungarian name (Cathrene). Norbert is hungarian as well as german name (exactly as written). I guess - but i'm not sure of course - this explains why the parents have chosen this name for him.