I think it was to suggest that one of his ancestors was willing to forsake the family name for reasons of expedience - that is, to suggest a kind of weakness of character - as well as to emphasize the distance between the branches of the family. If you were part of a close-knit family, you would probably be unwilling to change your last name to get an allowance or be remembered in a will, unless you cared more about money than you did your relationship with your brothers and sisters. I believe this was what Austen was implying.
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