There’s really interesting ways to look at the naming conventions for Ragtime.
Mother, Father, Younger Brother, are all archetypes. Silhouettes. They have rich stories and nuance and, at the same time, they are stand-ins for a white audience. It’s both centering in that their story is (while not the driving force of the plot) the running lens that the story returns to.
Tateh has a different name thrust on him that he can’t pronounce. He later takes on a different name, the Baron Ashkenazy, to lend himself more prestige. But in his heart and soul he continues to be Tateh. Papa. To his Little Girl. (Who also continues to have no name, who moved from set to set and time to time, who is harmed and benefits from Tateh’s attempts to give her Everything). Everything he does is because of wanting to protect and care for his daughter. (And contrasts to the character of Father who is Father in name only and certainly isn’t any good at being a Father.)
Sarah and Coalhouse Walker Jr. being named is an interesting contrast. It strips them of being archetypes in the ways that Mother, Father, and even Tateh provide. It turns them into fully-fledged humans with history and context. There was a Coalhouse Walker Sr. What is Sarah’s last name? We are told her family is from the south.
At the same time, being named strips them of being Father and Mother roles. They are humanized, and yet, they also are not given the benefit of being seen as silhouettes, as places for the audience to comfortably rest. Their story starts with pain and ends with pain. You rejoice in their love but know that their joy cannot last in this world. They are characters in history, either a lesson to learn from or a story of resilience to pass down. But they don’t really get to be the Mother and Tateh who raises the next generation, who the audience sees as their own grandparents and great-grandparents, comfortable and wisened.
Like Houdini and Nesbitt and Goldman, Coalhouse and Sarah are named. They are the driving force of the plot. But they aren’t the storytellers. They are the story.
(Some of this interpretation may or may not have been intended by the primarily white writers and creators of both the original book and the show. It’s mine.)