https://www.lds.org/topics/church-organization/the-church-of-jesus-christ?lang=eng&old=true
Christ’s Church Was Organized Again
On April 6, 1830, the Savior again directed the organizing of His Church (see D&C 20:1). Having received the priesthood keys, Joseph Smith now had authority to do this. During Christ’s mortal ministry, His Church was called the Church of Jesus Christ, and the members were called “Saints.” Now, in this later period of time, His Church is called The Church of Jesus Christ of Latter-day Saints (see D&C 115:4).