one’s reputation is justified (/well-deserved) ❍ 今得幸遇，真是～。(李汝珍《镜花缘》五十二回) Today I’ve met you here fortunately. I’ve found that your reputation as a scholar with real ability and learning is justified.
名下无虚mínɡ xià wú xū
名声大的人有真才实学；形容名不虚传。one’s reputation is justified, one’s reputation is well-deserved, have a well-deserved reputation