I always liked the way they came up with last names in such places as Iceland, where Eric's son became Ericsson and this daughter became Ericsdotter, or something like that.

But why just take the name of your father? My mother was a Clay, so maybe I should combine that with Murrill and become Murrclay.
I always suspected that names like Hoffmyer, were such combinations. Hoffman + Myers, maybe? Could Bowman and Jones become Bones? I once heard of a girl named Pigg who married a Hogg. Somebody probably made the story up, but wouldn't their children be happier growing up as Poggs or Higgs?
I never liked the hyphnated names like Smith-Jones. It would be better as Smones.

Sometimes names are shortened for convience. I suppose the Morton family could have once been the Throckmortens, and the Halls could have been Mindenhalls. I think many names that end in "stein" may have been shortened. Goldstein could have become Gold. I've known several people named Gold, but no, they weren't rich.

And then there is Indonesia where one name is enough. I once ran across an Indonesian named "Harry." That was it. No middle name, no last name. I understand that's the norm there.
Howard