Where did the name ''Judaism'' come from?

[Supervisor's note: All Israelite tribes were Jewish. The modern meaning of the word "Jew" is any adherent of Judaism, regardless of one's tribe. The following answer splits hairs, by using the strict and misleading definition that a Jew can only be a member of the tribe of Judah.]

Judaism is the term for the religion practiced by those of the tribe of Judah. Judah was one of the twelve sons of Jacob, whose name was changed to Israel in Genesis 29. Each of the twelve sons' families became a tribe; that is, each family grew so large that they were counted as a complete subset of the nation. When the Exodus happened, there were about 3 million people leaving Egypt, therefore each family would have had about a quarter of a million in it's roster.
Judah's tribe was the one tribe that converts to the nation of Israel joined. The name Judah means praise, so Judaism litterally means the people of praise. In the book of first Kings in the JudeoChristian Bible the division of Israel into the Southern Kingdom and the Northern Kingdom left the Southern Kingdom comprised of the tribe of Judah and Benjamin and Levi. Since Levi has no land inheritance, Judah and Benjamin were the landholders. When the Assyrian Army carried off the 10 northern tribes, all that was left of ancient Israel was Judah and Benjamin and Levi. Since Judah was the larger tribe, the custom became to call Israel by the larger tribe...Judah. The Hebrew word for this grouping is Yehudim, from which we anglicise into Jew; hence the name Judaism.
that is all correct but for one thing it was the Romans who gave the name Jew to us they came to israel and found most of the peoepl callign themslef fro mthe tribe of judea so they called the peopel judea which eveolved into Jew and so forth

• Answer:

1) Dictionaries define Judaism as the religion of Moses. All of the twelve Israelite tribes practiced the religion which we today call Judaism. The word comes from "Judah" because most Jews, but not all, are from that tribe. But the religion itself belonged not only to Judah.
2) We call someone Jewish not just because of genealogical descent, but also because of their beliefs and observances. "Anyone who opposes idolatry is called Jewish" (Talmud, Megillah 13a). It is in that sense of belonging to the Jewish religion that members of Israelite tribes other than Judah are called Jewish. Therefore, any attempt to go technical based upon specific tribes, is disingenuous and misleading. No one today would claim, for example, that today's Kohens and Levites are not Jewish.

Hebrews, Israelites and Jews are all one people, in different eras.

"Jews" refers to the people from the end of First Temple times, up to this day, because after the Assyrian conquest the Israelites who remained in the land were (and are) mostly from the Israelite tribe of Judah. But all the above terms are occasionally interchanged.

• Link: The twelve tribes today
  

In earlier times:

"Hebrews" (Ivrim) means descendants of Eber (Ever). Ever was an ancestor of Abraham (Genesis ch.10-11) and the earliest Hebrews were Abraham's uncles and cousins for several generations back. They were among the Western Semites and lived in northern Mesopotamia, near the confluence of the Balikh and the Euphrates.
Abraham (18th century BCE) was called a Hebrew (Genesis ch.14) because of his wider family.

Poetically, however, Abraham himself is called Hebrew because that name (Ivri) also translates to "the other side." Abraham was figuratively on "the other side" since he was the only monotheist (Midrash Rabbah 42:8) until his teachings took root. His ancestors and cousins had slipped into idolatry well before his time, as is evident from Genesis 31:30, 31:53, and Joshua 24:2. For that reason, Jews do not bestow on them the honorific title of ancestors despite the genealogical connection.
We credit Abraham as our first ancestor despite knowing exactly who came before, since it was Abraham who founded our beliefs. Thus, "Hebrews" is often used to mean Abraham and his Israelite descendants, instead of his wider family. In this sense it can refer to the Jewish people.

• Link: Abraham's biography
  

The word "Hebrews" can continue to refer to Abraham's descendants until the lifetime of Jacob. After that, we prefer "Israelites," since Jacob was given that name by God (Genesis ch.35), and it is considered a national title; one of honor. "Israelites" refers to the people (Jacob's descendants) down to the Assyrian conquest (133 years before the destruction of the First Temple), some 2600 years ago. After that, those that remained were called Jews (as explained above).

See also the Related Links

Link: Jewish history timeline

Link: Jewish ancestry