I don't think that the people always necessarily themselves
choose to use their second name - it's probably been instigated by their parents. I think maybe for reasons of the same names being used across families, as in naming patterns etc. or just naming after a chosen person..
Or, I dunno, lots of reasons I suppose, although my friend has a sister everyone calls Paula, and her registered name is Olga! Olga was a name further back in her father's family, and "had" to be used. But her Mum didn't like it, had wanted her named Paula - so she was Paula!!
I suppose too that most births would have been registered by the "man" of the house, so mother probably didn't get much of a "legal"say anyway!!
So there's always more than one way to "skin a cat"

Jeanne