1867, "calf or yearling found without an owner's brand," a word from the great cattle ranches of the American West, so called for Samuel A. Maverick (1803-1870), Texas cattle owner who was notoriously negligent in branding his calves.
All neat stock found running at large in this State, without a mother, and upon which there is neither mark nor brand, shall be deemed a maverick, and shall be sold to the highest bidder for cash, at such time and place, and under such rules and regulations, as the round-up commissioners of the district shall prescribe. [act to amend the General Statutes of the State of Colorado, approved April 8, 1885]
The family name is an old one in Boston, and a different Samuel Maverick was killed in the Boston Massacre. The sense of "individualist, unconventional person" is said to be attested by 1886, via the notion of "masterless," but its modern popularity seems to date to the late 1930s and the career of Maury Maverick (1895-1954) of Texas, grandson of Samuel the rancher and a Democratic congressman 1935-1939 famous for his liberal independent streak, who also coined gobbledygook.
"The Crisis" (April 1939) wrote that "During his stormy career in Washington Maverick became known as the one dependable liberal among the southerners. He recognized the broad problems of our nation, refusing to allow his vision to be limited by sectional prejudices, or racial or economic bugaboos. He was the only southern congressman to vote for the Gavagan federal anti-lynching bill. Not only did he vote for it, but he made a speech on the floor of the House in support of it."