Fannin County is a county in the far northeast of the U.S. state of Texas, on the border with Oklahoma. As of the 2020 census, its population was 35,662. The county seat is Bonham. The county was named for James Fannin, who commanded the group of Texans killed in the Goliad Massacre during the Texas Revolution. James Bonham sought Fanni…Fannin County is a county in the far northeast of the U.S. state of Texas, on the border with Oklahoma. As of the 2020 census, its population was 35,662. The county seat is Bonham. The county was named for James Fannin, who commanded the group of Texans killed in the Goliad Massacre during the Texas Revolution. James Bonham sought Fannin's assistance for the Battle of the Alamo, but Fannin was unable to provide it.