In modern times, they’re known as Carter and Shiera Hall, with Shiera donning the Hawkgirl mantle.
Carter was originally an ancient Egyptian prince named Khufu, but in the following millennia, he and his lover Chay-Ara have been reincarnated in numerous forms and eventually learn about their past lives.
Both are able to fly thanks to a special harness made from the alien element known as Nth metal.
Hawkman has one of the more complicated backstories in DC Comics canon, but presumably Black Adam will feature the Carter Hall incarnation, who debuted in the comics in 1940’s Flash Comics #1 and was one of the founding members of the Justice Society of America.