What connotations does Miss Scatcherd's name suggests in Jane Eyre?

This is an unpleasant name that sounds like scratch or scat, which is animal droppings. This fits Miss Scatcherd, a cruel teacher who victimizes the good Helen Burns. Jane thinks very poorly of her.
Miss Scatcherd seems to have her claws out, ready to scratch at and bully Helen about very petty things:

Burns, you are standing on the side of your shoe; turn your toes out immediately. [. . .] Burns, you poke your chin most unpleasantly; draw it in. [. . .] Burns, I insist on your holding your head up; I will not have you before me in that attitude.

Later, she turns even meaner, again over a small error on Helen's part:

You dirty, disagreeable girl! you have never cleaned your nails this morning!

For this, Miss Scatcherd beats Helen twelve blows on the back with a bundle of twigs, a punishment that seems far out of proportion to the very minor crime. Miss Scatcherd, a bully and a sadist, seems to have some serious anger issues, which she takes out on Helen, who won't fight back.
When Jane asks Helen about all this and why she tolerates Miss Scatherd, Helen defends her and says she is guilty of the faults the teacher names. Jane will have none of that, however, and offers a much more robust philosophy rather than merely accepting injustice meekly—a philosophy she has already used in her own life when she fought back against the cruel John Reed:

If people were always kind and obedient to those who are cruel and unjust, the wicked people would have it all their own way: they would never feel afraid, and so they would never alter, but would grow worse and worse. When we are struck at without a reason, we should strike back again very hard; I am sure we should—so hard as to teach the person who struck us never to do it again.