That's how they hide. When they move into a new nation, they adapt their surnames to sound like locals.

For example, in Croatia, they directly replaced their jewish surnames with local preexisting surnames, so you can't ID them by surname alone unless they are "foreign" jews. They did this in a lot of other European countries too, and it was not done by intermarriage, just direct surname theft.

First off, the -stein -berg names aren't even their real names.

Those are the names taken to imitate Europeans, so they could hide among they and pretend to be part of that population. The names you see them use in public are not their real names.

You've got it. They just picked German names at random, because the savages didn't use surnames until Christendom forced them to.

https://www.chabad.org/library/article_cdo/aid/4825070/jewish/10-Keys-to-Understanding-Many-Ashkenazi-Surnames.htm

At one point in the history of, what we know as German today, a king (or prince idr) made surnames mandatory.

Can't remember the bulk of the details, someone will fill the rest of them in.

Stein is stone in German.

Rothschild is literally Red Shield.

Burg/Berg, etc is just large city or people place.

The names are primarily of German origin and were adopted by Jews living in Germany. They were often known as the Yiddish (and also why the Yiddish language can be understood by people who speak the German language). This is why 'Yid' is sometimes used as a pejorative against Jews. When the Third Reich rose many of the Yiddish fled Germany. When they arrived in the U.S. (and elsewhere) their family names were put into official government record.

Prior to this vast, intrusive governmental record keeping apparatus it was easy for people to change their identity by simply moving somewhere they were unknown and making what ever claim they wanted. Many people joined the Roman patrician class through this method. There is a story (probably apocryphal) about a general serving under Julius Caesar who was shown to be an escaped slave and Caesar turned him over to his owner.

My guess is that a lot more jews used to live in Germany.

They use names which have no defined origin and can be applied to as broad a population as possible. Stein and Berg are place names which were so common there could be tens of thousands. They mesh by simply using largely applied names

Don't forget the cases where a typically first name is used as a last name (e.g. George Michael). These are almost always (((suspicious))).

They made these last names up in Germany to blend into the population, they so they exact same thing in the west with names like Green, Gold, ect.