What is the significance of Mrs. Sparsit's name in Hard Times?
You are right in identifying that Dickens uses names extremely interestingly to suggest aspects about his characters. Thomas Gragrind, for example, obviously suggests something about this character and his approach to education and what he does to children. One way to consider what the name of a character suggests about them is to consider the role they play in the novel and their characteristics.
Mrs. Sparsit, therefore, is Bounderby's housekeeper, who goes to live at the bank appartments when Bounderby marries Louisa. Once a member of the aristocratic elite, Mrs. Sparsit fell on "hard times" after her marriage collapses. Her defining characteristics are her selfishness, her dishonesty and the way she manipulates to get what she wants. It is clear that her overriding ambition is to destroy Bounderby's marriage to Louisa so she can marry him herself. Note how constant reference is made to her background, especially by Bounderby. In a sense, she acts as the opposite to Bounderby, having started off with a high social position and then sunk down into poverty, whereas Bounderby (supposedly) has made the same journey but in the opposite direction.
Considering these characteristics, it is clear then that "Sparsit" indicates and points towards the kind of miserly nature that embodies Mrs. Sparsit - miserly in both her character and with her finances. Her good qualities are "sparse" and her activities and attributes show that her character itself is very limited to her own self-serving interests.