I've now found a surname that is probably the original, Hochheimer, a surname much more common than Horkheimer. Hochheimer is a habitational name for someone from Hochheim, Germany. More variants I have found are Hirchheimer, Hirschheimer, Hochkammer, and Hoheimer, as you can see here
http://search.ancestry.com/cgi-bin/sse.dll?gl=allgs&gsln=Hochheimer&gspl=52&gss=seo&ghc=20 . The surname Hirchheimer and Hochkammer are not found in Germany, so maybe they are variant spellings of Hochheimer, a surname mostly found in Germany. The name hoch means "high", and so the name Hochheim means, "high settlement". This means that Horkheimer is actually a variant of Hochheimer, also as Hockheimer. The word Hock could also derive from Hoch also.
The name "Hork" alone seems unusual. While doing research on the surname Hork, I found that Hork was a Swedish name, and a Dutch name. The Dutch form is Van Der Hork, and the Swedish form is Hörk, but I don't know their meanings yet though. The name Heimer is also a Swedish surname, so Horkheimer could possibly be Swedish. The downfall is that I could not find the form Hörkheimer, so maybe not. The reason why I say unusual because this surname Hork is quite rare in Germany, and not much German surnames contain "Hork" as the first element. The few I've found were Horkstrom, Horkenbach, and Horkman. Horkman and Horkstrom are only found in the U.S., so perhaps an English form of a German surname. This lead me to conclude that Hork is actually a variant, and the closes connection I could see was Hock/Hoch. Because of the pronounciation of Hork in German, sounding like "huhk", I've found the surname Hockheimer, and later Hochheimer, Hochheim.
You were wondering where was my source. Well, to tell you the truth, I am mostly the source. I did not find any sources or mentionings about the name Hork and its origins, or Horkheimer, so I began to do research myself based on database I've looked into like
http://www.ancestry.com/,
http://worldnames.publicprofiler.org/Default.aspx, and many others. Many times I come across surnames that have been researched by other people who mentions their origin, but there are some that I cannot find, and those I look into. Saying that Horkheimer is a variant of Hochheimer all came from me, based on similarities, and as for evidence(somewhat), you can look here, one I posted above.
http://search.ancestry.com/cgi-bin/sse.dll?rank=0&gsln=Hochheimer&f7=WI&gss=genfact&db=1920usfedcenhttp://search.ancestry.com/cgi-bin/sse.dll?gl=CEN_1900&gsfn=William&gsln=Hochheimer&gss=angs-g&so=2http://search.ancestry.com/cgi-bin/sse.dll?gl=allgs&gsfn=Marie&gsln=Hochheimer&gss=seo&ghc=20Perhaps this was what you were looking for. This is all just a hypothesis, but a strong one I think.
This message was edited 12/8/2012, 6:56 PM