Many tourists come to this time-honoured shop because of its name.
Tips
usage
慕名 almost always comes right before a verb of coming or visiting: 慕名而来 "to come because of the fame", 慕名前往 "to go there because of the fame", 慕名拜访 "to call on someone one admires". 慕 is "to admire" and 名 is "fame".