Dory Maud is the owner of the shop Fathom & Sons, even though she has neither a last name nor any sons. She lives with her two sisters, Elizabeth and blind Annie, who also have no last names. They're the local color of the novel, giving Thisby a little sass but not actually affecting the plot of the novel in any way.
For some reason, Puck makes teapots and sells them at Dory Maud's shop. We never see her making teapots or receiving any money from this, so it's a pretty fruitless affair. Puck seems excited by the prospect of Dory Maud's catalog, which will sell products to the mainland, but by the end of the book, Puck has her Scorpio money and seems to have forgotten teapots and Dory Maud even exist. We almost forgot she existed, too.