Not everyone identifies strongly with their ethnicity or religion. I know many Jews that would consider themselves lots of things before “Jewish.” I think maybe some of my friends know that my dad is Jewish and wouldn’t be surprised if they forgot, because it’s not something that comes up a lot. If it weren’t for our last name, no random acquaintance would guess anything was Jewish about us without being told.
I’ve read many fascinating stories about about how people managed to avoid getting deported to the camps. But did it happen that someone went unnoticed by the nazis, because they didn’t have jewish relatives where they lived, didn’t go to temple, didn’t have a Jewish name, etc?
There are a few past answers on the subject that discuss this question here- short answer, it would have been very difficult, and personal identification with Judaism was rarely a factor.