Narrative: One again we have Nephi repeating himself. He tells us once again that we cannot err because of the way that he has presented the information,, but does not use this phrase as a parallel that emphasizes a point. Indeed, the logical construction of this sentence is convoluted.
To this point in Nephi's discourse he is promoting two themes simultaneously, and this dual purpose detracts from a single, focused argument. Nephi must not only tell us of the future history of Israel (and the role his message will play in it), but as part of that future history, Nephi takes a moment to discuss not only the mission of the Savior (which is a pertinent part of the future history) but also his testimony of that Savior. While it is understandable that he should bear testimony of Christ it provides a divergent focus from his point and results in a wandering argument line as well as this convoluted sentence.
Nephi gives his testimony of Christ with an oath. It is the strongest oath he can make, and he begins it with the ritualistic: "as the Lord God liveth." He then expands his oath with a reference t Moses, The reason for the reference to Moses is to provide a touchstone of accepted fact on which he can reference his oath. Nephi used Moses is a somewhat similar way in a speech to his brothers earlier in life (see the argument begun in 1 Nephi 17:23). In both that earlier speech and the current context, Moses is used as an undisputed historical fact. For Nephi, Moses is a historical fact so well accepted that he may use it as t he reference point for things that might not be assumed to be as historical.
In the earlier speech, the historical fact of Moses and the exodus was used as an indisputable fact that his brothers could not deny and therefore had to stand in condemnation for not likening there own situation to the Exodus led by Moses. In this case, the historical fact of Moses becomes the measure of the veracity of the oath Nephi pronounces.
The miracle of raising the serpent on the pole has christological meanings for modern readers, but Nephi is not using the incident for its typological meaning, but rather its evidential value as a proof of the power of the Lord through a prophet. The evidence that we should understand the example in this way is that Nephi gives two examples in his oath, and the delivery of water from the rock is much less obvious as a type of Christ. In the current context, it is the miracle rather than the meaning of the miracle that is important to Nephi. Even though the ultimate purpose of this passage is to declare Christ, Nephi does not explicitly use the incident of the raising of the serpent to move that argument forward.
Anthropological: Leaving aside for a moment the controversy over using Jesus Christ as name, the use of this oath places Nephi's use of "name" in an ancient context. In the ancient word, the one's name was more than a simple appellation, it was an intimate link to the person so named. In the Hebrew world, this extended to the changing of names in sacred circumstances where the nature of the person had changed, such as when Abram was renamed Abraham by the Lord.
This intimate connection between name and person is the reason for the modern idiomatic remnant of this concept. When we say "speaking of the devil" we meant that we have been speaking of a person, and that person arrives. In the origin of that idiom, the power of speaking the name would invoke the presence the presence of the person. In other words, the connection between name and person was considered to be so strong that the very utterance of the name could command the presence of the person so named.
Similar conceptions of the name and person exist in other cultures. The Navajo do not speak the name of the deceased, presumably for the reason that so speaking might call them from their rest to the known world.
It is this powerfully charged atmosphere that we do best understand Nephi's assertion that "there is none other name given under heaven save it be this Jesus Christ, of which I have spoken, whereby man can be saved." Note that even in the statement he makes, Nephi is referring to the person, not simply the name. Nephi says that there is "no name,,, save it be this Jesus Christ..." In the context of the question of the "name Jesus Christ" the presence of the word "name" in this sentence should be seen in the ancient context, and the "Christ" as the artifice of the translation process.
Remembering that the invocation of the name is the same (anciently) as the person helps us also understand that for us it is the mission and actions of Jesus that are salvific, not our conception of a label. To take upon us his name is to take upon us his efforts and presence, and therefore implies more of us than a simple declaration of him. The name implies the acceptance also of the requirements and yoke he places upon us, however light that yoke might be.