When they took upon them the name of Christ, they became like the high priests in the old temple, for the high priest wore on his forehead, literally, the name of Jehovah, and there was a promise in Numbers 6:27 that the Lord’s countenance would smile upon his people and that he would put his name upon them. This was an important step in the progress of these disciples, as they took the name of God upon themselves and enter into a covenant to keep these promises.
This meant that they had entered into a covenant to serve only one God, and especially not Mammon. This promise caused them, at the end of 3 Nephi, to put all their property together, and to have all their things in common. They did this because they had made a covenant that they would consecrate whatever the Lord had given to them. They had made a promise that their eyes would be single to his glory. They had covenanted that they would lay up treasures in heaven.
At the end of 3 Nephi, Jesus asked what the disciples would like: “What is it that ye desire of me, after that I am gone to the Father?” Three of them said that they would like to stay on this earth and teach more people. They were willing to offer all that they had to have a fullness of joy with Heavenly Father. The other nine wanted to stay with the Lord, and we understand that. However, the three who stayed behind, postponing their own spiritual progress in that way in order to be servants, were also keeping the covenant that they made to serve, to minister, and to continue to enjoy the blessings of seeing people helped as they come unto Christ.