General synonyms:
* Fame (can be either positive or negative)
* Infamy (specifically negative fame)
* Repute (general opinion or belief about someone or something)
* Renown (widely known and admired)
* Eminence (high standing or distinction)
More specific synonyms:
* Scandal (a public disgrace or offense)
* Infamy (being widely known for something bad)
* Disrepute (loss of respect or reputation)
* Notoriety (being widely known, often for negative reasons)
* Celebrity (being widely known and recognized)
The best synonym for "notoriety" will depend on the context of your sentence.