Give a dog a bad name
Definition 1 of 2
Pro Tip 1/3Metaphorical Use
The phrase is often used metaphorically to discuss reputation, not actual dogs. 
Once you give a dog a bad name, it's hard to clear it.
Pro Tip 2/3Negative Emotion
Using this phrase implies a strong negative emotion towards the action of harming reputation. 
He didn't just criticize her; he gave the poor girl a dog's bad name.
Pro Tip 3/3Social Consequences
The phrase emphasizes the long-term social damage of rumors or slander. 
In our small community, to give a dog a bad name is to ruin someone's social standing.