I'm pretty sure this used to work, but it doesn't seem to be now, unless I'm doing something wrong.
It looks like it does in fact change, but not on the screen you're on (unless you refresh). In other words, if you change the name and then click "Save Style", it loads that page again with a message that says "Success: Your style has been saved.". At this page, the name in the box is the old one still. However, if you reload this page, or go back to the list of styles, you'll get the new name. Because of this behavior, I'm actually thinking it's Firefox saving the form info rather than a bug in ScrapBook. But surely there must be a way force it to refresh the form data so it's right?