No, actually "dai" is NOT a japanic imperiallic notation. Age of empire of Korea, "ㅐ" pronounced as /äi/. So the early romanization of korean write "ㅐ" as "ai". and hyundai just accept it. when the "ai" notation still alive in 1947. But yeah, "Hyeon dae" is the right notation. and the company ignores it yet.
Not just cars, Hyundai is a Chaebol, a Korean conglomerate, and like all Korean conglomerates are highly diversified, they are the world's biggest ship builder, but also run their own fleet of ships, in addition to cars they build trucks, armoured fighting vehicles, industrial and construction plant, they provide food services, run hotels and own a soccer team (Ulsan Hyundai FC) and a baseball team (Hyundai Unicorns) and the list can go on.