As I stated in my Emperor Julius Caesar Alternate History post, I have memories from an actual Alternate History!
Out of respect for the wonderful literary creations and hypothetical scenarios involving time travel here, I will offer an imaginary scenario that I believe is likely the cause of the majority of Surname differences found between my Historical Timeline and this one.
Infamous due to the horrible media propaganda surrounding it, the Mandela Effect's Berenstein vs Berenstain Bears.
On my parallel historical timeline, it was without a single doubt in my mind, Berenstein! Even as a young child I knew enough to know Stein was a German beer drinking mug. So in my mind when I read the name Berenstein, they were "Beer drinking Bears!"
I always say, "If Einstein changed to Einstain, would you doubt the fact, for a single second, that it had been Einstein?"
Ellis Island was a common entry point for European immigrants entering at New York! So I hypothesize that in my timeline the Berenstain family arrives. The Immigration and Customs officer there sees the suffix "stain", and decided to "do them a favor," and did what was within his job's power, changed it to the more common suffix, Berenstein! A moment of kindness to prevent generations of teasing and adolescent torture! Lol
Here on this timeline, maybe the Immigration Officer had been on duty for 8 hours and was going on autopilot! He saw Berenstain, and it was just another name, not caring a bit about the negative connotations, he left it the way it was!
Another family the Schulz arrives, the agent noticed that it wasn't the more common, Schultz. Decided to give them a "much larger extended family" and changed it to Schultz. In my universe Charles Schultz was the creator of Peanuts! Not Schulz.
This is how many of the surname differences happened in my opinion. Different Immigration agents picking different Americanized Surnames!