应该是 have a reputation for sth. (= havethe reputation of) 意思是 ”因...而著名“ 或 ” 赢得...的名声“。例如：
He had a reputation for being bloody-minded and difficult. 他为人刻薄、难相处是出了名的。
They have a good reputation forf airness. 他们因公正而赢得了良好的信誉.
You have stained the goodr eputation of our family. 你坏了我们家的名声