The problem here is whether the original took is acting as the simple past-tense form of the verb take (“which … took upon themselves the name of Lamanites”) or as the past-participial form (“which had … took upon themselves the name of Lamanites”). The editors for the 1920 LDS edition interpreted took as the past participle; they therefore grammatically emended took to the standard past-participial form taken. For another example of this same editorial decision, see under Alma 8:26. For some other examples of this same conjunctive construction in the original text, see under 1 Nephi 1:14. The critical text will, of course, restore the earliest reading here in Helaman 11:24, “and took upon themselves the name of Lamanites”, irrespective of how took should be interpreted. In each case of took versus taken, the critical text will follow the earliest textual sources. For further discussion of past-participial took, see under past participle in volume 3.
Summary: Restore the original verb form took in Helaman 11:24: “and took upon themselves the name of Lamanites”; this verb form may be either the simple past-tense form took or the equivalent of the standard past-participial form taken.