Iraan, Texas. Iraan (/ˌaɪərəˈæn/ EYE-ra-ANN) is a city in Pecos County, Texas, United States. The population was 1,229 at the 2010 census. It was named for Ira and Ann Yates, owners of the ranchland upon which the town was built. Iraan is the second-largest town in the second-largest county in the second-largest state.