The town was named after W.T. Evans, a blacksmith. Evans settled in the area in 1902, and built a successful ranch. From 1918 to 1920, portions of the ranch were sold to the Socony-Mobil and Texas Oil Companies.
Geography
Evansville is located at . According to the United States Census Bureau, the town has a total area of, of which, of it is land and is water.
As of the census of 2010, there were 2,544 people, 967 households, and 637 families living in the town. The population density was. There were 1,109 housing units at an average density of. The racial makeup of the town was 90.8% White, 0.4% African American, 1.7% Native American, 0.4% Asian, 4.1% from other races, and 2.6% from two or more races. Hispanic or Latino of any race were 12.5% of the population. There were 967 households, of which 40.2% had children under the age of 18 living with them, 41.0% were married couplesliving together, 16.8% had a female householder with no husband present, 8.2% had a male householder with no wife present, and 34.1% were non-families. 23.5% of all households were made up of individuals, and 6.2% had someone living alone who was 65 years of age or older. The average household size was 2.63 and the average family size was 3.11. The median age in the town was 29.1 years. 28.9% of residents were under the age of 18; 12.9% were between the ages of 18 and 24; 31.2% were from 25 to 44; 19.9% were from 45 to 64; and 7.3% were 65 years of age or older. The gender makeup of the town was 49.6% male and 50.4% female.
2000 census
As of the census of 2000, there were 2,255 people, 848 households, and 561 families living in the town. The population density was 879.7 people per square mile. There were 918 housing units at an average density of 358.1 per square mile. The racial makeup of the town was 90.07% White, 1.11% African American, 1.24% Native American, 0.22% Asian, 4.43% from other races, and 2.93% from two or more races. Hispanic or Latino of any race were 8.43% of the population. There were 848 households, out of which 39.2% had children under the age of 18 living with them, 41.3% were married couples living together, 17.9% had a female householder with no husband present, and 33.8% were non-families. 25.8% of all households were made up of individuals, and 6.7% had someone living alone who was 65 years of age or older. The average household size was 2.66 and the average family size was 3.15. In the town, the population was spread out, with 32.1% under the age of 18, 13.7% from 18 to 24, 28.6% from 25 to 44, 18.4% from 45 to 64, and 7.2% who were 65 years of age or older. The median age was 27 years. For every 100 females, there were 90.5 males. For every 100 females age 18 and over, there were 88.9 males. The median income for a household in the town was $25,375, and the median income for a family was $28,603. Males had a median income of $26,536 versus $17,981 for females. The per capita income for the town was $11,657. About 21.4% of families and 25.9% of the population were below the poverty line, including 35.2% of those under age 18 and 15.4% of those age 65 or over.