Obsession with personal reputation is one of the many kinds of monomania presented in Bleak House. There are those whose social rank entitles them to limitless respect, which they don't hesitate to claim. There are also those whose position in life is the product of a fevered imagination – but this does not deter their posturing. The more either of these types demand respect, the more they seem to get it, perhaps because in a highly stratified society, it is always helpful to know who outranks whom, and that calculation is sometimes so hard to perform that it's easier to just go by a person's actions.
The only characters whose reputation precedes them are ones who are malicious or evil. Positive characters, on the other hand, have to reassert themselves and their intentions every time they encounter a new person.
The only characters whom it is possible to genuinely respect in the novel are ones who are narrated at least in part by Esther's voice. Anyone who is only described by the third-person narrator is shown with too many gaping flaws to be a figure of respect.