Date Discrepancies between Civil Records 
and the 
known Biographical detail of Jews

A major puzzle  for Jewish Genealogists and trap for those Jewish Genealogists is the problem with the "date of life events" of Jews. 
Dates of civil events for Jews as they are recorded in civil and state records prior to the 19th century can often appear to be at odds with the biographical detail known about those Jews. For example the date of a marriage is noted in civil records as being some times many years after children were born or after their biographical data says they were married. It should be noted that in many area’s civil and church authorities restricted activities by Jews. Marriage by Jews was restricted either to a certain number per year, or per community or upon payment of fees and taxes and sometimes not at all. Given the animosity and often down right racist (Anti Semitic) attitude, laws and restrictions of the Church and Civil authorities, many Jews through the ages just ignored the civil registration process - so a genealogist may not find a civil record.
Thus Jewish people did not necessarily register their marriages with the church or government. Jews got around these restrictions by performing their marriages according to the law of "Moses and Israel" or "al pi’ Halachah" - in accordance with Halachah / Jewish Law (in the presence of a Rabbi, 2 eidim (witnesses), and under a Wedding canopy (Chuppah) after exchange of a contract (Ketubah). It is certainly understood that all religious Jews and most assuredly rabbinical families lived lives observant of the Torah and Halachah.

An example is the second Gerrer Rebbe, Rabbi Yehuda (Aryeh) Leib Alter (the Sfas Emet) who was married according to Jewish Law but his civil marriage record appears many years after that, and after the birth of many of his children.

Children with the Mothers Family Name:
One result of this was that children often carried their mothers family name