Immigrant ship manifests are extremely valuable sources for most American Jewish genealogists. It is important to remember that these lists were compiled before the ship landed. Thus these lists contain the European, pre-Americanized names. You will find no Jewish "Jenny"s or "Harry"s among them — Those are American names.
For Jews from Eastern Europe, the names used on the passenger manifests will be the secular Yiddish names. The names were written down the way that they sounded, in the phonetics of the language of the ship.
Note that Jewish immigrants in the U.S. would often 'Americanize' the names of their parents on civil records (such as civil marriage and death certificates, Social Security Applications, etc.) -- even if their parents never immigrated. For example, an immigrant whose parents' names were Nochum and Chana might tell an American government clerk that their names were 'Nathan' and 'Anna' — even though they were never known by those names.