Surname prefixes

We say “Beethoven” but “Ludwig von Beethoven”; we say “Gadhafi” but “Moammar el-Gadhafi.”
What criteria determine whether a prefix will appear with a last name when the first name is also used?

Common usage or the preferences of the person involved. According the the Chicago Manual of Style (the “bible” for book publication):

“Both the spelling and the alphabetizing of these [compound] names should follow the personal preference of, or accumulated tradition concerning, the individual, as best exemplified in Webster’s Biographical Dictionary.”

Generally German names are not customarily written with the “von,” though there are probably some exceptions.

“East is east and west is west and if you take cranberries and stew them like applesauce they taste much more like prunes than rhubarb does.” – Marx

Read “Sundials” in the new issue of Aboriginal Science Fiction.

Sometimes the prefixes are or were part of the name - especially when they are remnants of a time that predates surnames. For instance the Welsh ap as in Daffydd ap Owain, the Hebrew Ben or Bar as in Barak Ben Canaan, the Scottish Mc or Mac as in Donald MacDonald, the Irish O as in Sean O’Flynn, etc. etc. all mean ‘son of’ or variations there of.
Sometimes a prefix is a designation of nobility, too. Friedrich Stueben, who helped train the Continental Army was the grandson of a minister who wanted to appear as something more so the family shoved a ‘von’ in there for status sake.
There are scads of books on the subject and origins of names and naming out there.