Clausen is a Danish patronymic surname, literally meaning child of Claus, Claus being a German form of the Greek Νικόλαος, Nikolaos, (cf.
[1] The spelling variant Klausen has identical pronunciation (as does the often interchangeable Claussen).
The two variants are number 34 and 85 on the top 100 of surnames in Denmark.
[2] Occurrences of Clausen/Klausen as a surname outside Denmark and Schleswig-Holstein are due to immigration.
Immigrants to English-speaking countries sometimes changed the spelling to Clauson.