I would agree that there is likely a variety of conventions depending on family origins.
So those with a Norse origin might well develope the use of -son, and -dottar ( -daughter).
While the nickname issue trends across all origins and classes.
Anglo-Saxons, tended to run a first letter, see the Cirdicingas for example and might in the longer run want to emphasise their roots to the founder of their clan/house.
So possibly something like "Cerdicsmægþ" (though I think that would imply the female side).