Some dialects of Macedonian (a language closely related to Serbo-Croatian) - mostly in Southern Macedonia (now in Greece) - still use the archaic word "duma" (äóìà) which means thought/thinking. My guess is that the person that founded your family was a thinker, and maybe got a nick-name Duma, hence his family were called Dumovi (of the Duma), and later it changed to Dumovich. At least, that's a common etimology of surnames I met in Macedonia.