The Danish surname Boer has the same entomology as the German / Jewish name Bauer. It was essentially a status surname, meaning either "peasant" or "neighbor." The name came originally from the Middle High German word "bur," referring to a small dwelling or building, which it turn evolved from the Old High German word "buan," meaning "to cultivate."
In the United States, the name Boer is the 17,438th most popular surname with an estimated 2,487 people with that name.  However, in Netherlands, the name Boer is ranked the 56th most popular surname with an estimated 14,774 people with that name. 
^ Filby, P. William, Meyer, Mary K., Passenger and immigration lists index : a guide to published arrival records of about 500,000 passengers who came to the United States and Canada in the seventeenth, eighteenth, and nineteenth centuries. 1982-1985 Cumulated Supplements in Four Volumes Detroit, Mich. : Gale Research Co., 1985, Print (ISBN 0-8103-1795-8)