Saginaw is a small city in Tarrant County, Texas, United States, and an Inner suburb of Fort Worth. The population was 23,890 in 2020 cens…Saginaw is a small city in Tarrant County, Texas, United States, and an Inner suburb of Fort Worth. The population was 23,890 in 2020 census. Saginaw is a Home rule municipality. The town was renamed Saginaw in 1882 by Jarvis J. Green, who had lived and worked on Saginaw Street in Pontiac, Michigan. The name Saginaw comes from the Ojibwe language and means "to flow out." It is also the name of a river, a bay, and a city in Michigan.