Most Jewish males have two names — a religious name, called the shem hakodesh, and a secular name, called the kinnui in Hebrew.
The religious name is a Hebrew name, and the secular name is in whatever vernacular language is in use. Observant American Jews today have a religious Hebrew name, and a secular English name. Among the Jews of Eastern Europe, Yiddish was the everyday or secular language, so they had a religious Hebrew name and a secular Yiddish name, the kinnui. In France, the secular name is in French; in ancient Babylonia, the kinnui was in Babylonian; etc.
After immigration to a new country, a new secular name was chosen, in the secular language of the new country. For most genealogical research, we need to know an ancestor's secular name, because this is the name (or some variant thereof) that appears in civil documents. The shem hakodesh, the Hebrew name, generally appears only in connection with Jewish religious observances, e.g., a record of a bris (circumcision), in a ketuba (marriage contract) or get (writ of divorce), and on a matzeva (tombstone).