I have noticed at least a couple of cases in my research in which a
family has a son, Movsha X, and then later another son, X (e.g. Movsha
Jankel and then Jankel), where I know for sure that neither of these
names are the patronymic or the father's patronymic.

Has anyone else seen this before? Any ideas on what this could signify
as far as naming patterns/traditions?

Thanks,
Josh Kaufman
Washington, DC