The word Hebrew comes from the Hebrew word Ivri (עברי). It's theorized that this word is related to the Hebrew word ever (עבר) which means "beyond". It's a reference to Abraham coming from "beyond the river".
Answer:
The name "Hebrews" comes from Ever (see Genesis ch.10), and refers to all of Ever's descendants, one of whom was Abraham (Genesis ch.11).
However, once we received the name of Israel (Genesis ch.35), we preferred to use that name instead of "Hebrews," because "Hebrews" is generic, while Israel is a title of honor.
When Paul wrote the book of Hebrews, it was the year 61 C.E. Times were very difficult for the early Christians. The Jews were becoming more and more hostile towards the Christians (as evidenced by the hunting down of some of the Apostles).
Paul, a former Pharisee, was well versed in the Mosaic Law. He was able to present evidence of the fulfillment of Bible prophecies that were fulfilled by Jesus Christ, his life, his ministry and his death. His reasoning as a Jew to another Jew, using the Mosaic law as his basis, was something they could understand and relate to.
Paul's letter served as a source of encouragement to the former Jews, giving them a sound basis for maintaining their faith.
See the attached link for a review of the Book of Hebrews.
The original word for which "Hebrew" is a transliteration, is "Ivri". In the simple sense it meant that Abraham came from "Ever (Hanahar)", the far side of the Euphrates. It also signifies him as a descendant of Ever (Genesis ch. 11).
On another level, it hints that Abraham was, in his beliefs, opposed (Ever="other side") the polytheism that was then ubiquitous.
Because Abraham was descended from Eber (Genesis ch.11).
They were still called Hebrews or Hebrew people. But they were also called Israelites or the Children of Israel.
After Jacob was renamed "Israel" in Genesis 32, his descendants were called "the children of Israel" or "Israelites".
Israel
Israel is the home of Hebrews, but they are actually called Jews.
The faith of Israel The people of Israel The Nation of Israel The Hebrews The Israelites The children of Israel
In the past: Canaan. Today: Israel.
The Ancient Hebrews were known by several names, including: Hebrews (עברים) Israel (ישראל) People of Israel (עם ישראל) Children of Israel (בני ישראל) Jews (יהודים)
None of these. The home of the Hebrews was Israel. After the year 70 CE, when they were kicked out of Israel, The Romans renamed it "Palestine" (but the home of the Hebrews was never called Palestine).
The Hebrews never left. They are still here today, and they are now called "Jews". Most were expelled from Israel in the year 70, but in 1948 they re-established the state of Israel.
Judaism (from the Latin Iudaismus, derived from the Greek Ioudaïsmos, and ultimately from the Hebrew יהודה, Yehudah, "Judah"; in Hebrew Also called: Hebrews Israelites the Children of Israel the People of Israel
Israelites (Yisraelim in Biblical Hebrew), Hebrews (a term first used probably by Ancient Egyptians) and Bnei Yisrael ("Children of Israel") are all terms used for Jews before the Common Era.
It was original called the Land of Israel, then it was Judea and Israel, then it was Palestine, then it was the State of Israel.