Iraan is a city in Pecos County, Texas, United States. Its population was 1,055 at the 2020 census. The city's name is an amalgamation of th…Iraan is a city in Pecos County, Texas, United States. Its population was 1,055 at the 2020 census. The city's name is an amalgamation of the first names of Ira and Ann Yates, owners of the ranch land upon which the town was built.