A legacy hero is a type of character, usually a superhero, that is the descendant or relative of an already or previously existing hero who either inherits or adopts the name and attributes of the original.
One of the earliest examples of this character type was comic strip hero The Phantom, assumed to be immortal by his enemies--various members of a single family, the descendants of Christopher Walker.
The term is used most often to refer to characters published by DC and Marvel comics. Family franchises such as DC's Atom, Black Canary, Captain Marvel, The Flash, Green Lantern, Hawkman, Hawkwoman, The Ray and Robin or Marvel's Black Knight, Captain America and Captain Marvel have seen several characters take up the name and abilities of the original.
In the video games series, Assassin´s Creed, many of the game´s characters are descended from bloodlines of Assassins.
Legacy villain
In opposition, there have been legacy villains in fiction as well. In comics, examples are DC's Blockbuster, Captain Boomerang, and Clayface; Marvel's Green Goblin, Mysterio, and Venom.
One of the best examples exists in Disney's Gargoyles, as a multi-generational line of villains known as the Hunter, originates with the TV series' fictionalized depiction of the historic Gille Coemgáin of Moray as a boy. The young "Gillecomegain", as he is known within the series' storyline, is confronted by the evil female gargoyle Demona and slashed by her on his face, and the trio of slash wound scars on Gillecomegain's face, carried by him for the rest of his life as he seeks his revenge on the female gargoyle, becomes part of the Hunter disguise for succeeding examples of the Demona-hunting antagonists.