Gordon B. Hinckley
"As his followers, we cannot do a mean or shoddy or ungracious thing without tarnishing his image. Nor can we do a good and gracious and generous act without burnishing more brightly the symbol of him whose name we have taken upon ourselves." (Be thou an Example, p. 90 as taken from Latter-day Commentary on the Book of Mormon compiled by K. Douglas Bassett, p. 200)
The name that Benjamin gives his people is the name of Christ. They are to take upon them His name (Mosiah 5:8). He makes it clear that their receipt of this name is specifically tied to the covenant they made after hearing his sermon. The name is given to all you that have entered into the covenant with God that you should be obedient unto the end of your lives (Mosiah 5:8). At the most fundamental level, it is clear that every newly baptized member of the Church effectively does the same thing by taking upon them the name of Christ. However, the relationship between covenant making and receiving a new name has a deeper meaning to endowed members of the Church. This is the pattern being established by Benjamin. It is reminiscent of other scriptures which teach of the same principle:
'To him that overcometh will I give to eat of the hidden manna, and will give him a white stone, and in the stone a new name written, which no man knoweth saving he that receiveth it.' (Rev 2:17)
'the white stone mentioned in Revelation 2:17, will become a Urim and Thummim to each individual who receives one, whereby things pertaining to a higher of order of kingdoms will be made known;
And a white stone is given to each of those who come into the celestial kingdom, whereon is a new name written, which no man knoweth save he that receiveth it. The new name is the key word.' (DC 130:10-11)