I assume this confusion is because she mentions early on that her parents live in Kiev.
You have turned your back on Russia! You are an American now, a super hero! I have parents back in Kiev waiting for me to make them proud. I have not forgotten what the Black Widow is at her core— a spy!
Of course, even as she mentions her parents in Kiev she clearly identifies as Russian. Her whole introductory monologue is all about her pure and unsullied Russian identity; that’s why Natasha calls her rooskaya/русская, which means the Russian. Yelena trained in Moscow and initially appears as an fiercely loyal agent of that state.
Now, why would she have parents in Ukraine, then? It’s tempting to write this off as another geography gaffe, since Marvel is not so good at non-U.S. cultures, customs, or locations. But I don’t think this needs to be the case here: there’s a large Russian diaspora in Ukraine. A significant minority in Kiev identify as Russian. We don’t know if Yelena was born in Ukraine or if her parents simply live there now.
Yelena was likely born before the collapse of the Soviet Union, and when she was introduced in 1999, it hadn’t happened terribly long ago. I think the possibility of Yelena growing up as a Russian in Kiev adds some interesting context to her initial fierce patriotism, especially if her parents were among the minority of Russians in Ukraine that did not support Ukranian independence in 1991. It would explain, I think, some of Yelena’s anger at Natasha’s loss of her “true Russian” identity.
Panel from Black Widow #1, by Devin Grayson and J.G. Jones.