or
John ~ his son = Johnson?
or
David ~ his son = Davidson?
Answers:
vikings. Lief Eriksson. Lief Erik's son same with dutch
Scots and Irish. Ian McDonald, Ian son of Donald. Mac is same.
also in middle ages. if illegitimate, put Fitz in front of father's, if known, name. David Fitzwarren. David is the illegitimate son of a man named Warren.
this is common all the way back to the Bible. Joseph, son of Jacob, son of Issac, son of Abraham etc.
Hope I helped.