"one who refuses obedience to a superior or controlling power or principle; one who resists an established government; person who renounces and makes war on his country for political motives," mid-14c., originally in reference to rebellion against God, from rebel (adj.).
By mid-15c. in the general sense of "obstinate or refractory person." The meaning "supporter of the American cause in the War of Independence" is by May 1775; sense of "supporter of the Southern cause in the American Civil War" is attested from April 15, 1861.
The Civil War's rebel yell is attested from 1862, but the thing itself is older and was said to have been picked up by (then) southwestern men in their periodic wars against the Indians.
The Southern troops, when charging or to express their delight, always yell in a manner peculiar to themselves. The Yankee cheer is more like ours; but the Confederate officers declare that the rebel yell has a particular merit, and always produces a salutary and useful effect upon their adversaries. A corps is sometimes spoken of as a 'good yelling regiment.' [A.J.L. Fremantle, "The Battle of Gettysburg and the Campaign in Pennsylvania," in Blackwood's Edinburgh Magazine, Sept. 1863]
Rebel without a cause is from the title of the 1955 Warner Bros. film, a title said to have been adopted from psychiatrist Robert M. Linder's 1944 classic "Rebel Without a Cause," which follows the successful analysis and hypnosis of a criminal psychopath but otherwise has nothing to do with the movie.