Let's do a quick census just to cover the rest of the named people of the Shtetl who have a minor impact on the story.
Trachim B's wagon accident, on March 18, 1791, sets the course for Trachimbrod over the next 150 years. Heck, the town is named after him. No one finds his body who knows where he went. (Did he fake his own death? Wash out to sea? Flip burgers in Memphis, TN?)
The accident is witnessed by Hannah and Chana, the twin girls of the Well-Regarded Rabbi ("WHO TALKS LIKE THIS") and the good gefiletfishmonger (a portmanteau of the words "gefilte fish" and "fishmonger") Bitzl Bitzl R.
Nearby is the mad squire Sofiowka N, who masturbates all the time and rapes Brod.
Rounding out this cast of characters are Shloim W, the humble antiques salesman; the deceased philosopher Pinchas T, who somehow communicates from beyond the grave; and The Wisps of Ardisht, who sound like a religious sect like the Dervishes, but they're just heavy smokers. A "clan of artisan smokers" (3.9), in fact, who have smoke streaming off them even when they're not lighting up.
A few generations later, we meet Menachim, the father of Zosha, who marries Safran in 1941. He lives in the Double House, which is surrounded by scaffolding and always changing… kind of like the shtetl itself. The wedding between Zosha and Safran pretty much cements the records of all the Trachimbroders: the guest list includes anyone who is anyone in the shtetl, so anyone not on the list might as well not exist.
These characters serve to add some good local color to the story. And if you think about it, it's nice to know they once existed. Jonathan (the character) might be trying to write a story about his ancestors, but all these people had families who might want to read about their ancestors, too.