European and Asian Jellies: when someone gets citizenship in your country how do they or you refer to them?

What I mean is, let’s say a Japanese or Irish woman becomes an Italian citizen, it doesn’t matter what country or race to use in the example, would you call her Italian? Or, refer to her as an Italian citizen? Would she be thought of as a “real” Italian?

I realize this might vary by country. If you have an answer let us know what country you are talking about.