Question

A word for publishing comments that hurt a persons reputation

Answer 1

Bullying, teasing,cyber-bullying, gossip, gossipping, etc?

Answer 2

discredit (verb)
to harm someone’s reputation

slander (verb)
to say something about someone that is not true and is likely to damage their reputation

taint (verb)
to make someone seem less honest, morally pure etc

smear (verb)
to try to damage someone’s reputation by telling lies about them
disgrace verb
formal to harm the reputation of a person or group by doing something bad or immoral

cast aspersions (on)

to say or write things about someone that attack their character, work etc