notoriety
noun /ˌnəʊtəˈraɪəti/
  /ˌnəʊtəˈraɪəti/
[uncountable, singular]- the state of being famous for being bad in some way
- notoriety (for something) She achieved notoriety for her affair with the senator.
 - This make of car has a certain notoriety for rust problems.
 - notoriety as something He gained a certain notoriety as a gambler.
 
Oxford Collocations Dictionaryadjective- a certain
 - considerable
 - international
 - …
 
- have
 - achieve
 - earn
 - …
 
- notoriety for