Confused about Tandy...

When I first read through Sherwood Anderson’s “Tandy”, I was so focused on the blatant presence of drunkenness and drinking that a large majority of the rest of the story flew straight over my head. It wasn’t until, actually, until my third read-through of the story that the rest of the symbolism started to flare up in front of my eyes.
“Tom Hard, the father” (Anderson 120).
“…in the struggle with an appetite that was destroying him” (Anderson 120).
“Perhaps of all men I alone understand” (122).
The cadence of the overall piece—the diction, syntax, and imagery—is distinctly biblical. It’s riddled with the words of a man who is angry at the world for falling to Christianity, of an anti-preacher of sorts. And he “never saw God himself manifesting in that little child” (120). The irony, though, doesn’t stop there. Not only does his daughter  have God manifesting within her, but he has a complete stranger tell her to be—what is essentially—more than human.
And she takes it. At five years old this young girl who remains nameless throughout the piece demands to have a different name—she is no longer the girl she was previously, but instead, Tandy Hard.
And that’s where I had to stop and look; there are exactly two named characters in this story, Tom Hard and George Willard. Granted, the story itself is on the shorter side (just over three pages in my copy of the novel), but even within a piece that short, names can be given. But neither the young girl (otherwise referred to as Tandy) nor the drunken stranger have a name.
Change in name symbolizes a rebirth of a person, a change in identity and morals and truths, as it were. But what does a name change mean when the first name is unknown? That is a question that I don’t have the answer to—either as a writer or a reader or an analyst. What do you do with a character who changes names, but doesn’t tell you what they change from?
(So far, all I can really come up with is staring blankly at the book and scribbling really aggressive annotations in my book.)
But if change in name is a rebirth, maybe this is more of an initial birth. Tandy is five years old, but her mother is dead and her father doesn’t pay her much attention—the story seems to give the feeling that the young girl gets what she physically needs but is depressingly lacking in what she could use emotionally. So, by taking hold of the Stranger’s words, of his truth, could it be a birth?
Or is it the turn to a grotesque? After all, it isn’t until someone takes a truth as their own that they become one—or at least, that’s how it works in the eyes of the writer.
Honestly, reading this story analytically almost left me with more questions than answers, and I’m not sure that it’s very helpful, but it’s here… and I don’t know how to explain it.