According to the book History of Sanpete County, the name "Manti" was suggested by Isaac Morley and agreed on by Brigham Young. This was in 1850. Manti was incorporated on 6 Feb 1851, the third community incorporated in the Utah Territory. Earlier Manti was designated the county seat of Sanpete County when the county was created by the territorial legislature on 31 Jan 1850. I couldn't find any mention of the Manti Indian Farm though.