There are other meanings as well, deeper meanings that the more mature members of the Church should understand and ponder as he or she partakes of the sacrament.
It is significant that when we partake of the sacrament we do not witness that we take upon us the name of Jesus Christ. We witness that we are willing to do so. (See D&C 20:77.) The fact that we only witness to our willingness suggests that something else must happen before we actually take that sacred name upon us in the most important sense.
What future event or events could this covenant contemplate? The scriptures suggest two sacred possibilities, one concerning the authority of God, especially as exercised in the temples, and the other—closely related—concerning exaltation in the celestial kingdom… .
Willingness to take upon us the name of Jesus Christ can therefore be understood as willingness to take upon us the authority of Jesus Christ. According to this meaning, by partaking of the sacrament we witness our willingness to participate in the sacred ordinances of the temple and to receive the highest blessings available through the name and by the authority of the Savior when he chooses to confer them upon us… .
… Our willingness to take upon us the name of Jesus Christ affirms our commitment to do all that we can to be counted among those whom he will choose to stand at his right hand and be called by his name at the last day. In this sacred sense, our witness that we are willing to take upon us the name of Jesus Christ constitutes our declaration of candidacy for exaltation in the celestial kingdom. Exaltation is eternal life, ‘the greatest of all the gifts of God’ (D&C 14:7).
(Dallin H. Oaks, Ensign, May 1985, pp. 80–81, 83)