Here the 1953 RLDS edition replaced the determiner that with the. Elsewhere, the text has one more example of “that same X”, where X is a personal name:
But there are no examples in the text of “the same X”, where X is a personal name. Note, by the way, that the 1953 RLDS edition did not replace the that in Alma 49:16 with the, which suggests that the change in Alma 10:2 was a simple typo.
Summary: Maintain in Alma 10:2 the determiner that in the phrase “that same Aminadi”.