Textual: The simple description of this event is that a census is taken and all pledge their covenant except the children, who not only may not be accountable for their covenant, but also are already covered under Christ's atonement according to Benjamin in Mosiah 3:16. There may be more to this than the simple explanation, however.
Two aspects of this event are unusual. The first is that this is a complete census of the people, but the taking of this census appears to be in contradiction to the explicit statement in Mosiah 2:2 that a census was not taken because there were so many people. Of course this difference is easily explained as a difference in time and purpose. The declaration that a census was not taken comes at the beginning of the gathering, and possibly refers to a typical facet of the recurring ceremony. Once again, if this is a feast of the Tabernacles, or any version of the Israelite autumnal festivals the first census not taken would have been a part of the expected order of events, and expectation that was unfulfilled, and therefore notable.
This counting comes later in the ceremony, and has as its purpose a declaration of covenant rather than a census. This declaration would have two functions. The first is that the very act of physically responding to the question reinforces the personal covenant that was communally acclaimed. The other aspect, however, that was equally important and should not be missed, is that this "census" actually took the names of those entering into the covenant. As discussed earlier, the power of the name was tremendous, and the name of Christ was given to the people. In this action, the reciprocal is made explicit, and the name of the individual covenanter is given to Christ (through the intermediary of the king).
The second problematic aspect of this census is the timing. Taking such an exhaustive physical census would be time consuming, even with all of the people assembled together in one place. Just as the delivery of the text of Benjamin's words would require the distribution through literate servants, so too would the recording of the name require literacy. While the Zarahemlaites might have been universally literate, that would run counter to most ancient literate societies in both the Old and New World, but particularly the New World. Assuming even a slightly higher literacy rate than might be expected, this taking of the names would still require physically distributing scribes with recording instruments (including sufficient ink and paper).
The next event that follows in the text is the coronation of the new king, an event which likely occurs with substantial ceremony. This assembly of people is very clearly a multiple day event, but it is most probable that while the taking of the names occurred during the festival, while all were assembled, it probably did not begin and finish prior to the coronation, as that wold have delayed the coronation significantly. The ordering here is literarily motivated not historically explicit. The taking of the names symbolically follows the bestowal of the name and belongs with that event, however the actual event took place.
It is impossible to discern if this juxtaposition of the historical with the spiritual event occurs in Mormon's source or in Mormon' abbreviation. To speculate, however, it is more probable that Mormon is recording the events in the general order in which he finds them in his source. The spiritual significance of the taking of the names would have been very significant to the original historian, and Mormon' s treatment-in-passing suggests that Mormon did not see the reciprocal exchange of names as being as significant as the original participants would have. Additionally, to this point we see little evidence of Mormon consciously reworking his material. His abridging efforts appear to consist of creating the narrative ties between cited speeches. If that is his operational mindset, the symbolic reworking of the linking narrative would be out of place and therefore suggests that this was the order given by the original scribe.