Even in the Shire family names have not become "fixed" as can be best seen in Sam's family tree . His uncle Andy has the surname Roper from his profession his son Frodo is Gardner, Elanor married Fastred of Greenholm and their descendents are Fairbairns.
they do illustrate the normal origins of surnames... appearance, profession, location (other than relationship to others).
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“But Finrod walks with Finarfin his father beneath the trees in Eldamar.”
Christopher Tolkien, Requiescat in pace
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