Bible School in Rebeka's Day

Is it true that even in Rebekah's time Noah's grandsons were teaching Torah?

That depends on whether you are asking from a biblical-historical perspective or a Jewish rabbinic tradition perspective.

Biblically, there is no statement that Noah's grandsons were teaching Torah during the time of Rebekah.

The Torah itself was not given until the days of Moses, many generations after Rebekah.

So if by "Torah" you mean the Law given at Sinai, then the answer is no.

However, in later Jewish tradition, especially in the Talmud and Midrash, there is a belief that God's teachings were preserved before Sinai. One famous tradition speaks of a "house of study" (beit midrash) of Shem and Eber. 

Shem was a son of Noah, and Eber was his descendant. According to this tradition, the patriarchs learned God's ways from them.

Some rabbis even say that Jacob studied in the school of Shem and Eber before returning to Canaan. In that sense, Shem and Eber were viewed as teaching divine wisdom and traditions long before Moses received the Torah.

So:

Bible alone: No evidence that Noah's grandsons taught Torah in Rebekah's day.

Rabbinic tradition: Yes, there is a tradition that Shem and Eber preserved and taught God's instruction before Sinai.

Many Christian scholars regard the school of Shem and Eber as a valuable Jewish tradition, but not something explicitly taught in Genesis.

Interestingly, when Rebekah was troubled by the twins struggling in her womb, Genesis says:

"She went to inquire of the LORD" (Genesis 25:22).

Some Jewish commentators connect this inquiry with Shem's school, but the Bible itself does not say whom she consulted.

So the claim is true in later Jewish tradition, but not directly stated in Scripture.

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Are the names of shem and eber mentioned in the scripture like in the lineage of Noah to isaac?

Yes. Both Shem and Eber (Heber) are explicitly mentioned in the Bible as part of the genealogy from Noah to Abraham and Isaac.

In Genesis 10–11:

Shem was one of Noah's three sons (Genesis 5:32; 6:10; 10:1).

Shem's descendants are listed in Genesis 11.

Eber was a descendant of Shem.

The lineage in Genesis 11 is:

Noah → Shem → Arphaxad → Shelah → Eber → Peleg → Reu → Serug → Nahor → Terah → Abraham → Isaac

Luke's genealogy of Jesus also includes both Shem and Eber (Luke 3:34–36).

The name Eber is particularly important because many scholars believe the term "Hebrew" (עִבְרִי, Ivri) is related to his name, though there are different views on the exact connection.

What Scripture does not say is that Shem and Eber operated a school or taught Torah. That idea comes from later Jewish tradition (Midrash and Talmud), not from Genesis itself.

One interesting observation: If you add up the ages in Genesis, Shem lived for many generations after the Flood and was still alive during much of Abraham's lifetime. 

This fact may be one reason later Jewish tradition imagined Shem as a keeper of ancient divine knowledge. The Bible confirms that Shem lived a very long time, but it does not explicitly say that Abraham, Isaac, or Rebekah met him or studied under him.