The original text of the Book of Mormon frequently used a redundant pronominal subject to refer to an immediately preceding complex noun phrase, as in the following nearby examples that involve relative clauses:
Here in Mosiah 25:12 the complex noun phrase is quite long and involves two relative clauses: “those which were the children of Amulon and his brethren which had taken to wife the daughters of the Lamanites”. The original redundant they helps the reader recover the subject after processing this long noun phrase. The critical text will restore such usage whenever it is supported by the earliest textual sources. See the discussion under Mosiah 15:22 and Mosiah 16:5. For other examples of this kind, see under SUBJECT REPETITION in volume 3.
Also in this passage Joseph Smith deleted the subordinate conjunction when at the beginning of the passage. The scope of the original when-clause seems to have extended all the way down to the word therefore, which means that the original text explained that when these children had decided to reject their fathers, then they decided to call themselves Nephites. Thus the original when in Mosiah 25:12 increases the clausal dependency in this passage and should be restored.
The original text had quite a few examples of a complex when-clause followed by a logically related independent clause preceded by therefore. The following examples have been retained in the current text:
For additional examples of this kind of construction, but with as-clauses rather than when- clauses, see under Mosiah 23:12.
Summary: Restore the original when in Mosiah 25:12; this subordinate conjunction increases the dependency between the complex subordinate clause and the subsequent main clause in the passage (“therefore they took upon themselves the name of Nephi”); also restore the redundant subject pronoun they, which helps the reader to process the complex syntax in this sentence.