Adding to Tibor's insightful comment on Kovacs - with my own confusing family as object lesson:
My GGF Wenzel was a Kovacs born in 1851 (in Topolya). The 1848 revolution heralded a patriotic era of Magyarization in the Hungarian outlands. It has been difficult to track my GGF's ancestry, and my best interpretation in line with data so far is that his family previously went by Schmied (Schmidt), but they altered their surname in that period. Kovacs and Schmied both mean "smith" in Hungarian and German respectively.
This was after the historical lord-and-serf period when many families were named for occupations, and the Church would have frowned on such inconsistent informality by then. However, in an ethnically mixed frontier region with enhanced mobility, it stands to reason that people might refer to those of another ethnicity or originating from another village as "Peter the Smith" or "Matthew the Miller." And they might confuse, for example, a Serb for a Hungarian. Barring bold physical distinctions (not often as obvious as many believed back when), who's to know if a new neighbor from elsewhere spoke the truth? [... often fluently in multiple languages.]
My own supposition is that especially the landless "peasants" of Serb, Romani or other displaced backgrounds might blend less obviously into Catholic communities by adopting German or Hungarian surnames, pairing up with locals (like my German GGM) and pretending to be like everyone else; would the priest really know? My GGF found his way from Topolya to the hof estates around Grabatz and eventually to Zerne, where nobody would know him from Adam. The story goes that ethnic inter-marriage was frowned upon and infrequent. I suspect it happened somewhat more frequently (and less secretly) than people would have admitted.
My father has a pronounced "Balkans" (i.e., Yugoslav or Romanian) signature in his autosomal DNA evaluation. My Kovacs GGF is the only logical source, despite having a Hungarian surname and apparently descended from parents with a German surname. What's in a name?
... from Charlie Tiller