The name Nilsson is a boy's name of Scandinavian origin meaning "son of Nils". Nilsson and discussed in our forums with posts like "Destiny Extended Congrats Game (round 6)".
From the experts:
The son at the end of many Scandinavian names makes them more consistent with modern American name tastes. While Nilsson may be the proper Scandinavian form of the name, many English speakers will try to spell it Nilson or Nelson.