West Lake has long been celebrated, and tourists flock there without pause.
Tips
usage
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'.