Positive and formal. Used for places, institutions, brands, dishes, or people whose reputation has stood for years or decades. Not for brief or recent fame — use 名噪一时 for short-lived renown.
memory
负 here is not 'to carry a burden' but 'to enjoy / bear (a reputation)', as in 负有盛名. 久 = long-time, 盛名 = great fame. Literally 'long bearing a great name'.
