[Awar]

It depends on which people you know then. By "secular", you probably mean "city folk".
We've lived through communism here, and even during the time when nobody was allowed to practise religion, people knew who their cousins are. Let alone centuries of supressed christianity during Ottoman rule. So, I think it's something else you should be targeting with gluing "family" onto "religion".

Then again, during the time when church was the strongest, few people actually had the right to have surnames. All across Europe.