This chapter is the Savior's testimony concerning the operation of his Atonement and why the Church should be called after his name.
It is interesting that from the very beginning the disciples called the Church by the name of the Church of Christ, as indicated at the end of the last chapter, but when the disciples circulated away from Bountiful and into the outer regions they were criticized for using this very simple name. We are not told what alternative names were suggested but there was enough controversy over it that the disciples met together in prayer to get the Savior's instructions.
The Savior seemed surprised that the disciples could not defend their position in calling the Savior's church simply the Church of Christ. Notice that the confusion was not among the disciples but "among the people."