“名声的败坏”可以翻译为 "the tarnishing of one's reputation" 或 "the ruin of one's reputation"。
"tarnishing" 强调名声逐渐受损、失去光泽的过程，带有一种渐进和负面的意味。
"ruin" 则更直接地表达了名声被彻底摧毁或破坏的结果。
根据具体语境，可以选择更贴切的表述。例如：
The scandal led to the tarnishing of his reputation. （这场丑闻导致他的名声受损。）
His unethical behavior resulted in the ruin of his reputation. （他的不道德行为导致他的名声彻底败坏。）