Most of the folks my age use “Orthodox Christian.” Most people where I live know what you mean if you say “Russian Orthodox” or “Greek Orthodox.” I tried telling the hospital I was Orthodox Christian and they put “Greek Orthodox” on my information sheet anyway

Not that I am Greek or Russian… but I guess they had a place to check on the computer that said “Greek Orthodox.”
See in the metropolitan area I live near there are three Orthodox parishes. And this is what the populace refers to them as;
Russian Orthodox (OCA parish) church
Greek Orthodox church
The Orthodox Church out on 20th st. (which more often than not I think more people go to than the other two).
Even for Byzantine/Greek Catholics the name goes through periods of vogue, like bpbasil said.
Greek Catholic usually foots the bill around here, even if you are UGCC or Ruthenian. You hear Byzantine Catholic sometimes.
I even hear some people still call Church Slavonic “Greek.”
As in, “My aunt died, she went to St. John the BaptistByzantine Catholic/UGCC, the one on 50th street, not the one down by City hall, and they did the service in Greek.”
Greek meaning Church Slavonic.
Sometimes I still hear Slavonic, Russian, Ukrainian, Slovak still referred to “Slavish.”
Around here there were so many of us Eastern Europeans that immigrated at the same time. They all spoke different languages, but the w.a.s.p. people just called it “slavish” because they didn’t know nor care to tell the difference between Rusyn and say Polish or Slovak.
Greek Catholic was a national identity for many immigrants. It was who they were, and that meant more than who they were in communion with. You would have to have grown up with the old timers that are gone to understand what I mean.
Even the now OCA was the Russian Greek Catholic Orthodox Church in North America.
The American Carpatho-Russian Orthodox Diocese full name is
American Carpatho-Russian Greek Catholic Orthodox Diocese.
Why? Because at a particular time and place the people from say the former Austrian Hungarian province of Galacia basically identified themselves as Greek Catholics in the USA, regardless if they were Orthodox or Catholic. It was their rallying point, their ethnic identity (the concept of a defined country in the old world at the time was different than ours).
So everything was held at the Church/church hall. Their civic life and their church life were melded into their say, Ukrainian-ness or Greek Catholic-ness. It is still like that to a point, but not really. You should have seen it when I was a kid. My dad says I should have seen it when he was a kid.
It was just tons of people that were family or darn near family that all would go to Church together and then literally spend all their time together. Someone would get married, it’d be 3 days plus of just celebration. I mean, it was amazing. Food, aunts, uncles, cousins, etc… Where my generation sits at home, their generation all went to the church and church hall and spent lots of time together. It was their Church, and the social hall was their city hall, their place to drink some brews, the place where they all cooked enough food to feed the Canadian Army, basically the Church was the centre of it all.
Now almost all the elders are gone and everyone has basically moved far away.