Mølgård: 

The name Mølgaard is a very common name in Denmark.  In fact, .03-.06%  of the 5.5 million people living in Denmark today are named Mølgaard.  (See Denmark's top 250 Surnames).  Because the name Mølgaard originated as a placename, many people from all over Denmark have the same surname but are not related to one another.

Patronymics

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.