Increasingly a large percentage of non-frum people with Jewish names are goyim, and many persons with non-Jewish names are Jews. In America, most Jews have not had a frum ancestor for over a century, and unless they are “into” genealogy they have no way to determine if they are actually Jews. Intermarriage has been a major factor in western countries since the early 19th century. This means a movement doing “kiruv” has to understand that someone with a Jewish surname who claims Jewish ancestry probably is goy, and a someone with a non-Jewish name who says they have Jewish ancestors quite possibly is Jewish. The only exception are people whose families went “off the derekh” recently, meaning their halachic status is easy to determine. — This is also an interesting problem if you want to use a Shabbos Goy — On the bright side, if you hold than a non-frum marriage ceremony among Jews creates a valid marriage ( a problem since virtually no non-frum Jews bother with a “get”), meaning children born outside the initial marriage are mamzerim, the fact the non-frum Jews are increasingly goyim, means they probably should be seen as being “safek goy, safek mamzerim” (cf. Ethiopian Jews) which resolves the problem. One should also note that conversion of a person who becomes frum only to realize they aren’t Jewish is NOT a major problem (they already are Shomer Mitsvos) and avoids having to worry about the intimate behavior of long dead ancestors,.
