How did Jews get to Europe and have names that aren't Middle Eastern What origin is their new names that's not Middle Eastern?

Answer 1

They got to Europe by migration over the course of generations. Even in Second Temple times, there are records of Jewish communities in southern Europe and North Africa, with names and dates.

In olden times, last names were relatively rare or non-existent. First names were used alone or with a descriptive addition, such as Simon of Montpelier, or Simon ben (son of) David, or Simon the Blacksmith, or Simon longbeard. By the time that taking a family name became commonplace, Jewish people had already been in Europe for centuries; they often spoke the local languages, so in many cases they adopted names which reflect those languages. The same goes for the Sephardi Jews in North Africa and the Near East. These last names might be geographically-based (such as Bamberger and Epstein for Ashkenazim, or Toledano for Sephardim); they could be based on lineage (Abramowitz, Mendelson), or based on occupation (Fleischer and Kramer, for example, are occupations), or descriptive (Grossbard, Kurtzman). Additionally, in some places, like Prussia, Jews actually had to buy their last names. Prettier names like Rosenzweig would cost more than less-pretty names like Goldstein. It provided an additional mechanism to squeeze money out of the Jewish communities.

There are, of course, some names which are not from other languages: Cohen, Katz, Levi, Sofer.