Icelanders manage OK without surnames. They use patronymic (or sometimes matronymic) instead.
If Chakotay used this method and called his son Clyde, his son would be known as Clyde Chakotayson. If his daighter was Kathryn, she would be known as Kathryn Chakotaydaughter. Or the children might use their mother's first name as a matronymic.
Women are known all their lives by the name their were given at birth and never take the husbands' names.
Of course, in all likelihood, Chakotay would give his some an Indian name.
Neelix and Tuvok don't have last names.