It isn't in UK English - not in full, anyway. It gets used reasonably frequently when abbreviated to 'auto', especially in advertising and signage. I think automobile would generally be considered a bit stiff/formal or old-fashioned. I do think it gets used in full fairly frequently in the US though.
However, I do remember being told (I can't remember when, or who by, or whether they were native Greek speakers) that Greeks themselves never really used αυτοκίνητο that much either.
I remember being told by whoever it was that αυτοκίνητο was roughly equivalent to automobile, αμάξι to car and όχημα to vehicle.
So although that person may or may not have been correct, I'd personally also be tempted to translate αυτοκίνητο as automobile.
Well, I think in Greek αυτοκίνητο and αμάξι are equally used for car.
Also, I seem to have an issue with automobile. The word automobile in english seems to me like it would be more frequently used as an adjective, rather than a noun, a car. Anything that moves by it's own means. It might be just me, so I guess it wouldn't hurt to add it as a possible translation.
"Automobile" may be more formal than "car," but it is used and is correct. While more formal, it is by no means obsolete or unused. For example, if you are searching for a mechanic in the phone book, you would look for "automobile repair and service." If you needed to rent a car, the search would be "automobile rental." We also say "auto" and "motor vehicle." The term "motor vehicle," however, includes more than just automobiles. The adjective is "automotive."
"Well, I think in Greek αυτοκίνητο and αμάξι are equally used for car."
I've been starting to get the sense that there's a lot of regional variation in Greek, both within the country and also amongst the diaspora. I won't even mention Cyprus ;-)
Doesn't seem quite as bad as Arabic though, where you can have two small villages in Syria/Lebanon/Jordan sitting right next to each other, and they'll pronounce the same word quite differently.
Both "automobile" as shown here and "automotive" are used frequently in both AE and BE, see this from the Guardian and Forbes both recent: "Automotive industry | Business | The Guardian https://www.theguardian.com/business/automotive-industry" "Forbes - Auto Information and Automotive News - Forbes.com www.forbes.com/autos/"