give a dog a bad name 的意思是“一朝坏名声，十年洗不清；名誉一毁，万难挽回；人言可畏”。

【例句】
Give a dog a bad name and hang him is true in George's case. For no one ever has a good word to say for him now.
名声一坏就翻不了身。乔治的情况就是如此，现在谁也不替他说句好话了。

Well, give a dog a bad name and hang him, right?
嗯，人言可畏，一旦有了恶名就难以洗刷掉，不是吗?