one’s reputation is justified (/well-deserved) ? 今得幸遇，真是～。(李汝珍《鏡花緣》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.
名下無虛mínɡ xià wú xū
名聲大的人有真才實學；形容名不虛傳。one’s reputation is justified, one’s reputation is well-deserved, have a well-deserved reputation