The names "Berenstein" and "Bernstein" did not arise from any special family feeling about amber-colored rocks. Ukrainian Jews were compelled to assume a "German sounding" surname in 1787 and Lithuanian Jews were asked to follow suit in 1797. Their task: to choose a name that sounded German but that had personal significance to them.
(1) One Lithuanian branch of this family, calling themselves initially BERENSTEIN, combined "Berungia", medieval name for French Burgundy (Bourgogne), and "Liechtenstein" as places of the family's residence prior to its emigration into the Pale of Settlement. Members of my own Berenstein family also named daughters "Rea" after the ancient Roman region of "Rheatia" or "Reatia", which included Burgundy, Bavaria, and other adjacent mountainous areas, indicating that my particular branch of this family emigrated very early from the Levant into the Rhine region, possibly hundreds of years before the Christian era, as Rheatia as an official entity disappears with Rome itself before 500AD.
(2) BERENSTEIN/BERNSTEIN also deliberately alludes to the 7th century Hebrew exilarch, Bustenai ben Chanina (618-670 CE), from whom some Jews proudly claim descent, as Bustenai's descendents are related to the British and French royal houses through Princess Sophia, Electress of Hanover and mother of King George I of Great Britain. My own great-grandmother changed her name from Meyta to Dora after she settled in America to reinforce this identity: Dora/Dara was the name of the Persian princess who became the wife of Bustenai and the progenitor of the line that became Hannover.
(3) BERENSTEIN also alludes to the Yiddish "b'reinshtein", which combines the Hebrew prefix "b'", meaning "from"; the German "rein", meaning "kosher" or "clean"; and the metonymic "shtein", derived from the German "Scheuerstein", meaning "kitchen" or "hearth". "Berenstein" (and Bernstein, as the shortened form) thus also means "from a kosher family".
(4) As yet untested is the hypothesis that Albert EINSTEIN's family took its name from an abridgement of Berenstein--i.e., from "Bereinstein" to "Reinstein" or "Einstein". An "Einstein", on the other hand, is a stone mason. The Einsteins arose in the same general vicinity of Germany as the Berensteins/Bernsteins.
Bustenai's story is told comprehensively in "Bustenai" by Lehman, out of print but available at Amazon. Burke's genealogy states that Bustenai is the 37th great-grandfather of George I; the best online article about him is at www.jewishencyclopedia.org
I don't know about you, but all this makes me want to bring out the family portraits and polish up the family silver.