expression, noun-modifying (irregular)
famous; celebrated; worthy of the name
Fixed literary expression meaning 'living up to one's reputation' or 'truly deserving of the name'. Often used prenominally (名に負う～). The variant 名にし負う is also common.
See also: 名にし負う
He is a celebrated doctor, truly worthy of the name.
I want to see with my own eyes a famous sword that lives up to its reputation.
From 名 (name, reputation) + に (case particle) + 負う (to bear, to carry). Literally 'to bear the name', i.e., to live up to one's reputation. The exact historical derivation is uncertain, but it is a classical fixed phrase.