From Longman Dictionary of Contemporary Englishbig nameˌbig ˈname noun [countable] APFAMOUSa famous person or group, especially a musician, actor etc Poor attendance at the concert was put down to the lack of big names.
Examples from the Corpus
big name• The athlete-trainer had a successful business, a big name, a wife and a child in the Soviet Union.• None of the soloists are big names yet, but there's a lot of talent there.• He told me it was important for me to understand he was a very big name in his own town.From Longman Business Dictionarybig nameˌbig ˈname noun [countable] a very well-known person, company, product etcThe company has already signed up some big names to provide the content for its news service.The plan is supported by some of the biggest names in the US auto industry. 