‘Jew’ and ‘Jewish’ aren’t official terms. The technical term is ‘ben/bat yisrael’ (son/daughter of Israel).
The Bible relates that Mordechai of the Tribe of Benjamin was called ‘ish Yehudi’ (Jewish man), so the term apparently goes back to the Kingdom of Judah which included the Tribe of Levi and remnants of the other tribes.
I guess it's what I have gone by. Paul was the tribe of Benjamin but I don't think of him as a "Benjaminite" but a Jew.
At first i didn't understand Smittie's comment about Hebrew but I think i do now; it could be used as a synonym for Jew.