My research has shown that the surname Schaumburg despite being literally translated as "foam castle" in modern German, actually has it roots in ancient German meaning "castle that looks over the land" as the namesake for the "Die Schaumburg" castle that overlooks the Weser river.

Transitions seem to be that in the earliest days (circa the year 1000) it was spelled something like "Scoenborg" or "Scowenborg", then transitioned to "Schauenburg" ("schauen"=to look, "burg"=castle), and then eventually today's Schaumburg.

There seem to be variations on this that still exist within Germany (Schauenburg, Schaumburger, etc.), and well as many variations that probably came about due to changes during emigrations from Germany.

If you do web searches on Scoenborg, Scowenborg, Schauenburg, and Schaumburg, you will get many German sites that explain much of this history, and the territories at points in time known as "Schaumburg". There is an enscription on the old stone tower at Die Schaumburg over the Weser with the old German version "Scowenborg" used.

I'm not a professional geneologist or a German history expert - but these are observations based on my personal web and field research. If anybody has more authoritative information I'd be interested.