Little Big Man

In the present day (1970), 121-year-old Jack Crabb, the oldest living man in the world and residing in a hospice, recounts his plentiful life story to a curious historian. Among other things, Crabb claims to have had been a captive of the Cheyenne, a gunslinger, an associate of Wild Bill Hickok, a scout for General George Armstrong Custer, and the sole white survivor of the Battle of Little Bighorn.
Jack begins his story in a flashback to 1859 when he was 10 years old where he and his older sister Caroline (Carole Androsky) survive the massacre of their parents by the Pawnee, and are discovered by a Cheyenne brave who takes the pair to his village. Caroline escapes, but Jack is reared by the goodhearted tribal leader Old Lodge Skins. As Jack gets older, he unwittingly makes an enemy of another boy, Younger Bear; however, Younger Bear eventually owes his life to Jack since he saved his life from a Pawnee brave. Jack is given the name "Little Big Man" because he is short but very brave. In 1865, when Jack is 16, he is captured by U.S. cavalry troopers during a skirmish and renounces his Cheyenne upbringing in order to save himself. He is put in the care of Reverend Silas Pendrake and his sexually frustrated wife, Louise, who tries to seduce Jack. When he witnesses Mrs. Pendrake having sex with the soda shop owner, Jack leaves the Pendrake household, and religion.
The following year, Jack becomes the apprentice of the snake-oil salesman Merriweather. The two are tarred and feathered when their customers realize that Merriweather's products are fraudulent. One of the angry customers is Jack's now-grown sister, Caroline, with whom he reunites. She attempts to mold her brother into a gunslinger named the Soda Pop Kid. Jack meets Wild Bill Hickok at a saloon, and Hickok takes a liking to the young man. When Hickok is forced to kill a man in self-defense, Jack loses his taste for gunslinging and Caroline deserts him.
Another year or so later, Jack becomes a partner in a general store and marries a Swedish woman named Olga (Kelly Jean Peters). Unfortunately, Jack's business partner turns out to be a thieving scoundrel. The famous cavalry officer George Armstrong Custer suggests the couple restart their lives further west and assures them they have nothing to fear of Indians. They set out, but their stagecoach is ambushed by Cheyenne warriors. Olga is abducted and Jack sets out in search for her. He is reunited with Old Lodge Skins. Younger Bear has become a Contrary, a warrior who does everything in reverse. Jack makes friends with the hwame Little Horse, but continues on his search for Olga.
Jack eventually becomes a "muleskinner" in Custer's 7th Cavalry, only because Custer incorrectly determines that was Jack's past job. He takes part in a battle against the Cheyenne, but when the troopers begin killing women and children, Jack turns on them. Jack discovers a Cheyenne woman, Sunshine (AimÃ©e Eccles), giving birth. He returns with her to Old Lodge Skins's tribe. Sunshine becomes his wife and bears him a child. Jack again encounters Younger Bear, not a Contrary anymore, who is now the henpecked husband of the long-lost Olga. Olga does not recognize Jack, who makes no attempt to make her remember him. Sunshine asks Jack to take in her three widowed sisters as wives and to father children with them. He is reluctant at first, but finally agrees.
In November 1868, Custer and the 7th Cavalry make a surprise attack on the Cheyenne camp at the Washita River. A now-blind and elderly Old Lodge Skins is saved by Jack, but Sunshine, their child, and her sisters are killed. Jack tries to infiltrate Custer's camp to exact revenge, but loses his nerve to kill Custer.
Disheartened, Jack withdraws from life and becomes the town drunk living in Deadwood, South Dakota for the next several years. While in a drunken stupor, he is recognized by Wild Bill Hickok, who gives him money to get cleaned up. Hickok is shot and killed while playing cards and, with his last breath, asks Jack to bring some money to a widow he was having an affair with. Jack visits the widow, now a prostitute who turns out to be Louise Pendrake. Jack gives her the money that Hickok intended for her to use to start a new life, but again rebuffs her sexual advances. This scene provides an homage to Hoffman's role in the movie The Graduate and his seduction by Mrs. Robinson.
Jack soon becomes a trapper and hermit. His mind becomes unhinged after coming across an empty trap with a severed animal limb. He prepares to commit suicide, but sees Custer and his troops marching nearby, and decides to return to his quest for revenge. Custer hires him as a scout, reasoning that anything Jack says will be a lie, thus serving as a perfect reverse barometer. Jack tricks Custer into leading his troops into a trap at the Little Bighorn by truthfully telling Custer of the overwhelming force of Native Americans hidden within the valley. As Custer's troops are slaughtered by the combined Sioux and Cheyenne group, he begins to rave insanely. The mad Custer attempts to shoot Jack who is wounded, but is killed by Younger Bear, who then carries Jack away from the battlefield. Having thus discharged his life debt, Younger Bear tells Jack that the next time they meet, he can kill Jack without becoming an evil person.
Back at the Indian camp, Jack accompanies Old Lodge Skins to a nearby hill, the Indian burial ground, where the old man, dressed in full chief's regalia, has declared "It is a good day to die", and decides to end his life with dignity. He offers his spirit to the Great Spirit, and lies down at his spot at the Indian Burial Ground to wait for death. Instead, it begins to rain. Old Lodge Skins is revealed to still be alive, and says, "Sometimes the magic works, and sometimes it doesn't". They return to his tepee to have dinner.
Back in the present, Jack's narrative ends and he dismisses the historian. The final shot shows the elderly Jack thinking with sadness about the memories of a world which is no more.

Question: Because Jack is short and brave, what name was he given?
Answer: Little Big Man