Roosevelt is a city in Duchesne County, Utah, United States. The population was 6,046 at the 2010 census, with an estimated population of 7,070 in 2018. The proper pronunciation of the city's name …Roosevelt is a city in Duchesne County, Utah, United States. The population was 6,046 at the 2010 census, with an estimated population of 7,070 in 2018. The proper pronunciation of the city's name ROH-zə-velt is based on how President Theodore Roosevelt pronounced his name: according to the man himself, "pronounced as if it was spelled 'Rosavelt.'"