Using the priesthood authority they had received and following the example of the Master, the Nephite Apostles (and others) went forth ministering to the Church, setting it in order, and performing the essential ordinances for those who were being converted. This period of time was marked with great spiritual manifestations and remarkable peace and harmony among the Church of Christ.
“They… Were Called the Church of Christ”
Another word for church could be fold or even family. By taking the name of Christ upon us (see Mosiah 5:8) through his gospel and ordinances (see 3 Nephi 11:32-38) we come into the “fold of God’ (see Mosiah 18:8), and by the power of the Holy Ghost we are born again and become members of his family (see Mosiah 5:7). All of these requirements ensure membership in the earthly Church of Christ, but when coupled with continued faithfulness and valiance in the testimony of Jesus, as well as with the ordinances of exaltation found in temples, we become members of the heavenly Church of Christ—the Church of the Firstborn (see D&C 76:54; see also D&C 84:34).”