notoriety
Being well-known for something bad or shameful.
Notoriety means being famous for something bad or negative. When someone achieves notoriety, they become well-known, but not in a way they should feel proud of.
A student who constantly disrupts class might gain notoriety as a troublemaker. A criminal who commits a famous robbery becomes notorious (the adjective form). A restaurant might achieve notoriety for its terrible food or rude service. The key difference between notoriety and regular fame is the negative reason behind the recognition.
People sometimes confuse notoriety with fame, but they're quite different. An Olympic athlete has fame for their achievements. A cheater who gets caught has notoriety for their dishonesty. Both are widely known, but one is admired while the other is disapproved of.
When someone is notorious, they're marked out in people's minds, but not for reasons they'd want. Once you gain notoriety for something, it's hard to shake that reputation. A notorious liar finds that people stop believing them, even when they're finally telling the truth.