Why is Pearl an appropriate name for the character?
Pearl's name is appropriate for a number of reasons.
A pearl is traditionally symbolic of something of great value. Pearl is a child born in shame, looked upon as tainted or arguably of less value in Puritan society, yet by naming her Pearl, Hawthorne emphasizes her worth. Indeed, isolated from her peers, she is high-spirited and close to nature, standing out in contrast to the drab, constrained children of the Puritan elders. Dressed unconventionally in decorative clothing, she is a dynamic personality, shining brightly in the dull, gray landscape of her society.
Also, in the Bible, a pearl is compared to heaven, something man will strive to achieve at great cost (Matthew 13:44-45). Pearl likewise is conceived and born at great cost to her parents.
In chapter six, the narrator tells us that Hester named her daughter Pearl because she had been purchased with all she had - she was her mother's only treasure. This idea comes from a parable in the Bible found in Matthew 13 verses 45 and 46. In the parable, Jesus tells about a merchant who was seeking fine pearls. He finds one pearl worth more than all the others, and he goes and sells all he has to buy the one pearl. Hester 'sold' all she had and Pearl was all she had left. The narrator is careful to tell us that Pearl's personality does not match her name - she is not calm nor does she have "white, unimpassioned lustre", but she is a rare beauty which is indicated by the name.
In many ways, Pearl is a suitable name. First, a pearl is made when grains of sand mix in an oyster, out of ugliness something beautiful is made. Second, pearls have a glow or luster about them, not overtly shiny. Third, pearls, authentic ones, come at a great price. All of these could fit Pearl in the novel.
I think that Pearl is a good name for her because yes, she is everything of value to Hester and things along those lines that others have posted.
In addition, a Pearl comes from the pink of an oyster (a little graphic!) which is Hester. Oysters are bottom-feeders. This can be taken to mean that they are scum and garbage (Hester's self-loathing), or that they are filters. Filtering is taking something bad and making it better (Hester's self-worth). This leads to a theme that the worst treated in society are most often the most valuable.