About Jewishness

Sephardic Jews borrowed a very significant number of names from their Christian neighbors during the 11th to the 13th centuries.
Except for aristocrats, wealthy people and well off Jewish merchants did not get surnames in Eastern Europe until the Napoleonic years of the early 19th century. Most of the Jews from countries captured by Napoleon including Russia, Poland, and Germany were ordered to get surnames.
The reason for the last names were for tax purposes. After Napoleon's defeat many Jews dropped their surnames and returned to "son of" names like Mendelsohn, Jacobson, Levinson, etc. During the so called Emancipation, Jews were once more ordered to take on surnames. When Jews adopted family names in the 18th and 19th centuries, the choice was frequently the patronymic and first names thus became family names.
Russia has introduced law for surnames use for Jews in 1804, but in reality started enforcing this policy only in 1834.
In the 1700's Hebrew sounding names, like Yaakov ben Yitzhak, became forbidden in many countries where Jews were living. The bureaucrats produced lists of "acceptable" names. Bribes were necessary to secure "nice" family names, derived from flowers or precious stones: Lilienthal, Edelstein, Diamant, Saphir, Rosenthal. Two very expensive names were Kluger (wiser) and Fröhlich (happy). Most Jews were brutally lumped by bored officials into four categories and named accordingly: Weiss (white), Schwarz (black), Gross (big) and Klein (little). Many poorer Jews had unpleasant names foisted on them by malignant clerks: Galgenstrick (gallow's rope), Eselkopf (donkey's head), Taschengregger (pick-pocket), Schmalz (grease), Borgenicht (don't borrow), for example, or like in Holland, Geelhoed (yellow hat), Spanjer (from Spain), Vischkooper (fish buyer), etc. Jews of priestly or levitical descent, who could claim names like Cohen, Kahn, Katz, Levi, were forced to Germanise them: Katzman, Cohnstein, Aronstein, Rubenstein, Levinthal, etc. A large group were given places of origin: Brody, Epstein, Ginzberg, Landau, Shapiro (Speyer), Dreyfus (Trier), Horowitz and Posner. The pain of this humiliating procedure was not lessened by the knowledge that the government's main object in imposing it was to make Jews easier to tax and conscript.
The vast majority of Jews did not have fixed surnames in 1788 and so had to adopt one. Therefore it's hard to find details of previous years.

In the US until relatively recently, and certainly before 1900, you could call yourself anything you wanted.
Most states required that the selected surnames be in the language of the state, or at least that the names not be Biblical in some senses. The language of the Austrian Empire and of the Germanic states was German. The secular language of the Jews of central and eastern Europe was Yiddish, a language with substantial roots in medieval German. The language of the Russian Empire was Russian, a Slavic language. Thus the surnames of central and eastern European Jews sound Germanic or Slavic because they are.
Galician Jews have been compelled to adopt German sounding surnames on July 23, 1787 during Joseph II, Empress Maria Theresa's son rule, following the introduction in 1781 the first genuine reforms in Central Europe - Judenreformen und Toleranzpatent (Jew-reforms and Edicts of Tolerance).
In much of Germany, Jews did not have fixed surnames until 1812 or even later. At that time, German Jews took all kinds of surnames. Many of these names were based on the profession of the person taking the name. Someone who ran a small shop might well have called himself Kramer or Kraemer.

Most name changes came about as a result of the immigrant desire to Americanize names and this usually happened some time after arrival. Try comparing the passenger arrival record to what appears later in either city directories, or on naturalization papers. Also bear in mind that immigrants arrived with identification papers ... and in some cases those papers were false and can thus explain a name different that what the family name actually was at the time."
Another possibility: there might have been relatives in the US who recommended a name to your ancestor who came to the US on a ticket with the name, or it may have been changed any time later. In the early days (1900 included), there was no necessity of changing a name through a court order, one day someone would decide his last name sounded better as Morris than Manischewitz (or whatever), so he would just change it.

Ashkenazim did not name children after a living ancestor. That was as much a non-no as it was in Eastern Europe. Nor was there a hard-and-fast rule about whom children were named after; it was something worked out by the parents on the basis of those who had died, those who had already had a child named after them, the social or rabbinic standing of an ancestor, whose side of the family needed appeasement and so on--and often on the basis of a relative who had died in the months immediately preceding the birth.
Sephardic naming tradition is naming after living grandparents and other living family members. As a result, across a given generation, there were multiple repetitions of the same first name, since, not only could one set of parents name children after their four respective parents, but so could all their siblings use the same parent's name, as well as uncles' and aunts' names. The Sephardic tradition:
First son named after father's father; second son named after mother's father; first daughter named after mother's mother; second daughter named after father's mother.