It's hard to explain but sometimes people Latinized their names and changed the spelling to reflect the culture of the times and where they lived (not unlike how today some from other countries will change their names to sound more "American"). Oddly, occasionally a surname would be Latinized by the local priest. Because priests wrote in Latin back then they Latinized or if you will wrote the Latin version of the names. For example Paul became Palus (or a similar spelling). Surnames were no different. Sometimes the people themselves would use the Latin version of their names (usually for status).
The stories about religious persecution are very much true. Protestants were often persecuted by Catholic rulers and Catholics were often persecuted by Protestant rulers. Minorities like Jews and Anabaptists were persecuted by nearly everyone. It was one of the prime reasons why so many came to America in the 1600 and 1700's (but by no means the only reason).