In Denmark until about 1850-1870, most ordinary
people used patronymics instead of surnames. Patronymics are made
from the Christian name of a person´s father, followed by "sen"
(=son) or "datter" (=daughter). So, e.g. Jens Nielsens
daughter Maren´s full name would be "Maren Jensdatter".
And his son Søren would be "Søren Jensen".
Actually, patronymics were abolished by law in 1826.
The authorities wanted people to use family surnames instead. During the years 1828 -
1856 all families, by law, had to choose a family name. It could either
be a surname of patronymic origin (only -sen), a placename (village,
farm etc.), the name of their occupation or a popular callingname.
But it took several decades before patronymics
disappeared. So, for a person born from about 1826-1870 it is sometimes
impossible to tell whether a person's last name is a patronymic or a
family surname. (Unless of course you already know the parents of the
person in question!)
For more information on Danish names, see Danish
State Archives: Christian Names.