Old man Moses had two sons, David bar Moses in 1721 and Salomon bar Moses in 1723. David's firstborn, a daughter known as Sophie David Moses, Sophie Moses David or "die Davidin"—"the David girl"—wed, at 17, Isaak bar Veis (Isaak son of Veis) a widower from nearby Monzingen on the river Nahe. The other son, Salomon bar Moses, or Moses Salomon, adopted the name Salomon as a family name while Isaak's son by his first mariage, Liebmann Isaak, started the Liebmann family.

With David Moses' passing in 1802 without male issue, Isaak bar Veis assumed his father-in-law's name of Moses as a mark of respect and in order to assure the old gentleman that a male family member would be called upon in the synagogue to recite the "Kaddisch," the prayer in memory of the deceased.

Probably known as "Eisicks Moyshe," Isaak prospered as a cattle dealer and money lender. He and Sophie had three sons, Peter in 1789, Simon in 1792 and Michael in 1795. France annexed the Palatinate during the Napoleonic era, with Jews now granted most rights of citizenship, but obligated to adopt a permanent family name which could not, in these parts, be either Hebrew or a place name. Isaak Moses could no longer sign, in Hebrew "Raschi" script, as either "Isaak Moyses" or as "Isaak Becherbach" as heretofore. His real estate dealings in mortgages for big city investors created a paper trail of signatures, over time, of Isac Moses, Isaak Mosiz, then Isac Moriz and, ultimately, the Germanic Moritz, which appears on the Jewish census of 1819.

Fire destroyed a large part of the town in 1854, including the Jewish prayer room and part of the Eisick house. Shortly thereafter, the year 1856 saw the passing of both the brothers Peter and Michael, and the emigration to "Amerika" of Peter's widow, Adeline née Binnes, together with their son Gustav.

Moritz residence in 1938
The "Isidorschhaus," the Moritz ancestral family home in 1938
Hauptstraße 1, Becherbach-an-der-Großbach bei Kirn/Nahe

The family of the surviving Simon Moritz and wife Nanette, née Gottschall, continued to be known by the name of their house as "Eisicks," until a new large house was built on the main street—the "Hauptstrasse"—across from the Town Hall by Simon's son David (1821–1881) and grandson Isidor (1860–1908), after which the family became known by the new "Hausnamen" of "Isidorsch," which continues to be the case to this day.

Isidor wed Regina Wendel, of nearby Nahbollenbach, and fathered eight children, ere he passed away, in 1908, at the young age of 48.